Pub Date : 2024-08-11DOI: 10.1088/1742-5468/ad0635
Pierfrancesco Urbani
Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.
{"title":"Quantum exploration of high-dimensional canyon landscapes","authors":"Pierfrancesco Urbani","doi":"10.1088/1742-5468/ad0635","DOIUrl":"https://doi.org/10.1088/1742-5468/ad0635","url":null,"abstract":"Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1088/1742-5468/ad6428
David Martin, Gianmarco Spera, Hugues Chaté, Charlie Duclut, Cesare Nardini, Julien Tailleur and Frédéric van Wijland
The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.
在对齐自走粒子的集合体中，向集体运动过渡的性质仍是一个长期争论的问题。在这篇文章中，我们将重点放在干活性物质上，并证明微弱的波动足以将二阶平均场过渡转变为 "不连续 "共存情景。我们的理论展示了波动是如何诱发极场质量的密度依赖性的，即使这种效应在均场水平上并不存在。反过来，这种对密度的依赖会引发有序和平流之间的反馈回路，最终导致向集体运动的非均质过渡和非均质旅行带的出现。重要的是，我们证明了这种由波动引起的一阶转变既存在于粒子与相邻粒子在有限距离内对齐的度量模型中，也存在于 "拓扑 "模型中，其中对齐是基于更复杂的相邻集合构造。我们利用随机微积分对噪声引起的极场质量重正化进行了分析计算，并通过一回路场理论分析进一步予以支持。最后，我们通过对波动流体力学以及具有 k 近邻或 Voronoi 排列的拓扑粒子模型进行数值模拟，证实了我们的分析预测。
{"title":"Fluctuation-induced first order transition to collective motion","authors":"David Martin, Gianmarco Spera, Hugues Chaté, Charlie Duclut, Cesare Nardini, Julien Tailleur and Frédéric van Wijland","doi":"10.1088/1742-5468/ad6428","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6428","url":null,"abstract":"The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad6138
Indrani Bose
The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction of the output of a production function and the technology efficiency parameter , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital . We derive analytically the steady state probability distribution and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of We identify a critical value of below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.
{"title":"Growth, poverty trap and escape","authors":"Indrani Bose","doi":"10.1088/1742-5468/ad6138","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6138","url":null,"abstract":"The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction of the output of a production function and the technology efficiency parameter , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital . We derive analytically the steady state probability distribution and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of We identify a critical value of below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad5c5d
C Chatelain
The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically using the corner transfer matrix renormalization group algorithm. The critical exponents are known to depend on the chemical potential of vacancies, or monomers. At large average density of the latter, the phase transition becomes the first-order. We compute the scaling dimensions of both the order parameter and temperature in the second-order regime and compare them with the conjecture that the critical behavior is the same as the Ashkin–Teller model on its self-dual critical line.
{"title":"CTMRG study of the critical behavior of an interacting-dimer model","authors":"C Chatelain","doi":"10.1088/1742-5468/ad5c5d","DOIUrl":"https://doi.org/10.1088/1742-5468/ad5c5d","url":null,"abstract":"The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically using the corner transfer matrix renormalization group algorithm. The critical exponents are known to depend on the chemical potential of vacancies, or monomers. At large average density of the latter, the phase transition becomes the first-order. We compute the scaling dimensions of both the order parameter and temperature in the second-order regime and compare them with the conjecture that the critical behavior is the same as the Ashkin–Teller model on its self-dual critical line.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad5c5c
Harold Erbin, Riccardo Finotello, Bio Wahabou Kpera, Vincent Lahoche and Dine Ousmane Samary
Signal detection is one of the main challenges in data science. As often happens in data analysis, the signal in the data may be corrupted by noise. There is a wide range of techniques that aim to extract the relevant degrees of freedom from data. However, some problems remain difficult. This is notably the case for signal detection in almost continuous spectra when the signal-to-noise ratio is small enough. This paper follows a recent bibliographic line, which tackles this issue with field-theoretical methods. Previous analysis focused on equilibrium Boltzmann distributions for an effective field representing the degrees of freedom of data. It was possible to establish a relation between signal detection and -symmetry breaking. In this paper, we consider a stochastic field framework inspired by the so-called ‘model A’, and show that the ability to reach, or not reach, an equilibrium state is correlated with the shape of the dataset. In particular, by studying the renormalization group of the model, we show that the weak ergodicity prescription is always broken for signals that are small enough, when the data distribution is close to the Marchenko–Pastur law. This, in particular, enables the definition of a detection threshold in the regime where the signal-to-noise ratio is small enough.
信号检测是数据科学的主要挑战之一。在数据分析中，数据中的信号经常会被噪声干扰。有多种技术旨在从数据中提取相关的自由度。然而，有些问题仍然难以解决。尤其是在信噪比足够小的情况下，几乎连续光谱中的信号检测。本文沿用了最近的文献路线，用场理论方法解决这一问题。以往的分析侧重于代表数据自由度的有效场的平衡波尔兹曼分布。我们有可能在信号探测和对称性破缺之间建立一种关系。在本文中，我们考虑了受所谓 "模型 A "启发的随机场框架，并证明了达到或未达到平衡状态的能力与数据集的形状相关。特别是，通过研究模型的重正化群，我们表明，当数据分布接近马琴科-帕斯图尔定律时，信号足够小时，弱遍历性规定总是被打破。这尤其有助于在信噪比足够小的情况下定义探测阈值。
{"title":"A functional renormalization group for signal detection and stochastic ergodicity breaking","authors":"Harold Erbin, Riccardo Finotello, Bio Wahabou Kpera, Vincent Lahoche and Dine Ousmane Samary","doi":"10.1088/1742-5468/ad5c5c","DOIUrl":"https://doi.org/10.1088/1742-5468/ad5c5c","url":null,"abstract":"Signal detection is one of the main challenges in data science. As often happens in data analysis, the signal in the data may be corrupted by noise. There is a wide range of techniques that aim to extract the relevant degrees of freedom from data. However, some problems remain difficult. This is notably the case for signal detection in almost continuous spectra when the signal-to-noise ratio is small enough. This paper follows a recent bibliographic line, which tackles this issue with field-theoretical methods. Previous analysis focused on equilibrium Boltzmann distributions for an effective field representing the degrees of freedom of data. It was possible to establish a relation between signal detection and -symmetry breaking. In this paper, we consider a stochastic field framework inspired by the so-called ‘model A’, and show that the ability to reach, or not reach, an equilibrium state is correlated with the shape of the dataset. In particular, by studying the renormalization group of the model, we show that the weak ergodicity prescription is always broken for signals that are small enough, when the data distribution is close to the Marchenko–Pastur law. This, in particular, enables the definition of a detection threshold in the regime where the signal-to-noise ratio is small enough.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad613b
Miguel Mena, Solmar Varela, Bertrand Berche and Ernesto Medina
Here we review a universal model for chirally induced spin-selectivity (CISS) as a standalone effect occurring in chiral molecules. We tie together the results of forward scattering in the gas phase to the results for photoelectrons in chiral self-assembled monolayers, and the more contemporary results in two terminal transport setups. We discuss the ingredients that are necessarily present in all experiments to date, which we identify as: (i) chirality, be it point, helical or configurational, (ii) the spin–orbit coupling as the spin active coupling of atomic origin, (iii) decoherence as a time-reversal symmetry breaking mechanism that avoids reciprocity relations in the linear regime and finally (iv) tunneling that accounts for the magnitude of the spin polarization effect. This proposal does not discard other mechanisms that can yield comparable spin effects related to interactions of the molecule to contacts or substrates that have been proposed but are less universal or apply to specific situations. Finally, we discuss recent results suggesting CISS as a molecular phenomenon in the realms of enantiomer selectivity, coherent electron transfer, and spin effects in chiroptical activity.
{"title":"Minimal model for chirally induced spin selectivity: spin-orbit coupling, tunneling and decoherence","authors":"Miguel Mena, Solmar Varela, Bertrand Berche and Ernesto Medina","doi":"10.1088/1742-5468/ad613b","DOIUrl":"https://doi.org/10.1088/1742-5468/ad613b","url":null,"abstract":"Here we review a universal model for chirally induced spin-selectivity (CISS) as a standalone effect occurring in chiral molecules. We tie together the results of forward scattering in the gas phase to the results for photoelectrons in chiral self-assembled monolayers, and the more contemporary results in two terminal transport setups. We discuss the ingredients that are necessarily present in all experiments to date, which we identify as: (i) chirality, be it point, helical or configurational, (ii) the spin–orbit coupling as the spin active coupling of atomic origin, (iii) decoherence as a time-reversal symmetry breaking mechanism that avoids reciprocity relations in the linear regime and finally (iv) tunneling that accounts for the magnitude of the spin polarization effect. This proposal does not discard other mechanisms that can yield comparable spin effects related to interactions of the molecule to contacts or substrates that have been proposed but are less universal or apply to specific situations. Finally, we discuss recent results suggesting CISS as a molecular phenomenon in the realms of enantiomer selectivity, coherent electron transfer, and spin effects in chiroptical activity.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad64bc
P D Alvarez
We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.
{"title":"Exact partition function of the Potts model on the Sierpinski gasket and the Hanoi lattice","authors":"P D Alvarez","doi":"10.1088/1742-5468/ad64bc","DOIUrl":"https://doi.org/10.1088/1742-5468/ad64bc","url":null,"abstract":"We present an analytic study of the Potts model partition function on the Sierpinski and Hanoi lattices, which are self-similar lattices of triangular shape with non integer Hausdorff dimension. Both lattices are examples of non-trivial thermodynamics in less than two dimensions, where mean field theory does not apply. We used and explain a method based on ideas of graph theory and renormalization group theory to derive exact equations for appropriate variables that are similar to the restricted partition functions. We benchmark our method with Metropolis Monte Carlo simulations. The analysis of fixed points reveals information of location of the Fisher zeros and we provide a conjecture about the location of zeros in terms of the boundary of the basins of attraction.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad5c5a
M Romero-Bastida and A Poceros Varela
In this work, we conduct an extensive study of the asymmetric heat flow, i.e. thermal rectification, present in the two-segment Frenkel Kontorova model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. We have considered systems with both high and low asymmetry and determined that, in the weak-coupling limit, thermal rectification is larger when NNN interactions are relevant. The behavior of the heat fluxes as a function of the coupling strength between the two segments is largely consistent with a well-defined rectification for larger system sizes. The local heat fluxes present a very different behavior for systems with high and low asymmetry. The results of this work may help in the design of molecular bridges, which have recently been shown to be able to function as thermal rectification devices.
{"title":"Thermal rectification in segmented Frenkel–Kontorova lattices with asymmetric next-nearest-neighbor interactions","authors":"M Romero-Bastida and A Poceros Varela","doi":"10.1088/1742-5468/ad5c5a","DOIUrl":"https://doi.org/10.1088/1742-5468/ad5c5a","url":null,"abstract":"In this work, we conduct an extensive study of the asymmetric heat flow, i.e. thermal rectification, present in the two-segment Frenkel Kontorova model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions. We have considered systems with both high and low asymmetry and determined that, in the weak-coupling limit, thermal rectification is larger when NNN interactions are relevant. The behavior of the heat fluxes as a function of the coupling strength between the two segments is largely consistent with a well-defined rectification for larger system sizes. The local heat fluxes present a very different behavior for systems with high and low asymmetry. The results of this work may help in the design of molecular bridges, which have recently been shown to be able to function as thermal rectification devices.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad57b1
Guido Caldarelli, Andrea Gabrielli, Tommaso Gili and Pablo Villegas
The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification into a relatively small set of universality classes. The RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate interplay of correlations on multiple scales. Existing approaches have relied on hypotheses involving hidden geometries and based on embedding complex networks into hidden metric spaces. Here, we present a practical overview of the recently introduced Laplacian RG (LRG) for heterogeneous networks. First, we present a brief overview that justifies the use of the Laplacian as a natural extension of well-known field theories to analyze spatial disorder. We then draw an analogy to traditional real-space RG procedures, explaining how the LRG generalizes the concept of ‘Kadanoff supernodes’ as block nodes that span multiple scales. These supernodes help mitigate the effects of cross-scale correlations due to small-world properties. Additionally, we rigorously define the LRG procedure in momentum space in the spirit of the Wilson RG. Finally, we show different analyses for the evolution of network properties along the LRG flow following structural changes when the network is properly reduced.
{"title":"Laplacian renormalization group: an introduction to heterogeneous coarse-graining","authors":"Guido Caldarelli, Andrea Gabrielli, Tommaso Gili and Pablo Villegas","doi":"10.1088/1742-5468/ad57b1","DOIUrl":"https://doi.org/10.1088/1742-5468/ad57b1","url":null,"abstract":"The renormalization group (RG) constitutes a fundamental framework in modern theoretical physics. It allows the study of many systems showing states with large-scale correlations and their classification into a relatively small set of universality classes. The RG is the most powerful tool for investigating organizational scales within dynamic systems. However, the application of RG techniques to complex networks has presented significant challenges, primarily due to the intricate interplay of correlations on multiple scales. Existing approaches have relied on hypotheses involving hidden geometries and based on embedding complex networks into hidden metric spaces. Here, we present a practical overview of the recently introduced Laplacian RG (LRG) for heterogeneous networks. First, we present a brief overview that justifies the use of the Laplacian as a natural extension of well-known field theories to analyze spatial disorder. We then draw an analogy to traditional real-space RG procedures, explaining how the LRG generalizes the concept of ‘Kadanoff supernodes’ as block nodes that span multiple scales. These supernodes help mitigate the effects of cross-scale correlations due to small-world properties. Additionally, we rigorously define the LRG procedure in momentum space in the spirit of the Wilson RG. Finally, we show different analyses for the evolution of network properties along the LRG flow following structural changes when the network is properly reduced.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-30DOI: 10.1088/1742-5468/ad6137
Eren Metin Elçi, Timothy M Garoni
We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in both cases that this autocorrelation time is linear in the volume in the subcritical regime, but strictly sublinear in the volume at criticality. This establishes rigorously that the cluster size at the origin in these models exhibits critical speeding-up. The proofs involve controlling relevant Fourier coefficients. In the case of binary trees, these Fourier coefficients are studied explicitly, while for high-dimensional tori we employ a randomised algorithm argument introduced by Schramm and Steif in the context of noise sensitivity.
{"title":"Critical speeding-up in dynamical percolation","authors":"Eren Metin Elçi, Timothy M Garoni","doi":"10.1088/1742-5468/ad6137","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6137","url":null,"abstract":"We study the autocorrelation time of the size of the cluster at the origin in discrete-time dynamical percolation. We focus on binary trees and high-dimensional tori, and show in both cases that this autocorrelation time is linear in the volume in the subcritical regime, but strictly sublinear in the volume at criticality. This establishes rigorously that the cluster size at the origin in these models exhibits critical speeding-up. The proofs involve controlling relevant Fourier coefficients. In the case of binary trees, these Fourier coefficients are studied explicitly, while for high-dimensional tori we employ a randomised algorithm argument introduced by Schramm and Steif in the context of noise sensitivity.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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