Francesco Andreucci, Stefano Lepri, Carlos Mejía-Monasterio, Stefano Ruffo
We study non-equilibrium properties of a chain of $N$ oscillators with both long-ranged harmonic interactions and long-range conservative noise that exchange momenta of particle pairs. We derive exact expressions for the (deterministic) energy-current auto-correlation at equilibrium, based on the kinetic approximation of the normal mode dynamics. In all cases the decay is algebraic in the thermodynamic limit. We distinguish four distinct regimes of correlation decay depending on the exponents controlling the range of deterministic and stochastic interactions. Surprisingly, we find that long-range noise breaks down the long-range correlations characteristic of low dimensional models, suggesting a normal regime in which heat transport becomes diffusive. For finite systems, we do also derive exact expressions for the finite-size corrections to the algebraic decay of the correlation. In certain regimes, these corrections are considerably large, rendering hard the estimation of transport properties from numerical data for the finite chains. Our results are tested against numerical simulations, performed with an efficient algorithm.
{"title":"Thermal transport in long-range interacting harmonic chains perturbed by long-range conservative noise","authors":"Francesco Andreucci, Stefano Lepri, Carlos Mejía-Monasterio, Stefano Ruffo","doi":"arxiv-2409.11832","DOIUrl":"https://doi.org/arxiv-2409.11832","url":null,"abstract":"We study non-equilibrium properties of a chain of $N$ oscillators with both\u0000long-ranged harmonic interactions and long-range conservative noise that\u0000exchange momenta of particle pairs. We derive exact expressions for the\u0000(deterministic) energy-current auto-correlation at equilibrium, based on the\u0000kinetic approximation of the normal mode dynamics. In all cases the decay is\u0000algebraic in the thermodynamic limit. We distinguish four distinct regimes of\u0000correlation decay depending on the exponents controlling the range of\u0000deterministic and stochastic interactions. Surprisingly, we find that\u0000long-range noise breaks down the long-range correlations characteristic of low\u0000dimensional models, suggesting a normal regime in which heat transport becomes\u0000diffusive. For finite systems, we do also derive exact expressions for the\u0000finite-size corrections to the algebraic decay of the correlation. In certain\u0000regimes, these corrections are considerably large, rendering hard the\u0000estimation of transport properties from numerical data for the finite chains.\u0000Our results are tested against numerical simulations, performed with an\u0000efficient algorithm.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The energy landscape is central to understanding low-temperature and athermal systems, like jammed soft spheres. The geometry of this high-dimensional energy surface is controlled by a plethora of minima and their associated basins of attraction that escape analytical treatment and are thus studied numerically. We show that the ODE solver with the best time-for-error for this problem, CVODE, is orders of magnitude faster than other steepest-descent solvers for such systems. Using this algorithm, we provide unequivocal evidence that optimizers widely used in computational studies destroy all semblance of the true landscape geometry, even in moderate dimensions. Using various geometric indicators, both low- and high-dimensional, we show that results on the fractality of basins of attraction originated from the use of inadequate mapping strategies, as basins are actually smooth structures with well-defined length scales. Thus, a vast number of past claims on energy landscapes need to be re-evaluated due to the use of inadequate numerical methods.
{"title":"Mirages in the Energy Landscape of Soft Sphere Packings","authors":"Praharsh Suryadevara, Mathias Casiulis, Stefano Martiniani","doi":"arxiv-2409.12113","DOIUrl":"https://doi.org/arxiv-2409.12113","url":null,"abstract":"The energy landscape is central to understanding low-temperature and athermal\u0000systems, like jammed soft spheres. The geometry of this high-dimensional energy\u0000surface is controlled by a plethora of minima and their associated basins of\u0000attraction that escape analytical treatment and are thus studied numerically.\u0000We show that the ODE solver with the best time-for-error for this problem,\u0000CVODE, is orders of magnitude faster than other steepest-descent solvers for\u0000such systems. Using this algorithm, we provide unequivocal evidence that\u0000optimizers widely used in computational studies destroy all semblance of the\u0000true landscape geometry, even in moderate dimensions. Using various geometric\u0000indicators, both low- and high-dimensional, we show that results on the\u0000fractality of basins of attraction originated from the use of inadequate\u0000mapping strategies, as basins are actually smooth structures with well-defined\u0000length scales. Thus, a vast number of past claims on energy landscapes need to\u0000be re-evaluated due to the use of inadequate numerical methods.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"54 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The continuous injection of energy at a localized region in space in a stationary gas creates a shock wave that propagates radially outwards. We study the hydrodynamics of this disturbance using event driven molecular dynamics of a hard sphere gas in three dimensions, the numerical solution of the Euler equation with a virial equation of state for the gas, and the numerical solution of the Navier-Stokes equation. We show that the results from the Euler equation do not agree with the data from hard sphere simulations. Including dissipative terms through the Navier-Stokes equation results in reasonably good description of the data, when the coefficients of dissipation are chose parametrically.
{"title":"Shock propagation in a driven hard sphere gas: molecular dynamics simulations and hydrodynamics","authors":"Amit Kumar, R. Rajesh","doi":"arxiv-2409.12086","DOIUrl":"https://doi.org/arxiv-2409.12086","url":null,"abstract":"The continuous injection of energy at a localized region in space in a\u0000stationary gas creates a shock wave that propagates radially outwards. We study\u0000the hydrodynamics of this disturbance using event driven molecular dynamics of\u0000a hard sphere gas in three dimensions, the numerical solution of the Euler\u0000equation with a virial equation of state for the gas, and the numerical\u0000solution of the Navier-Stokes equation. We show that the results from the Euler\u0000equation do not agree with the data from hard sphere simulations. Including\u0000dissipative terms through the Navier-Stokes equation results in reasonably good\u0000description of the data, when the coefficients of dissipation are chose\u0000parametrically.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"187 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Molecular dynamics simulations offer detailed insights into atomic motions but face timescale limitations. Enhanced sampling methods have addressed these challenges but even with machine learning, they often rely on pre-selected expert-based features. In this work, we present the Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph neural networks and the State Predictive Information Bottleneck to automatically learn low-dimensional representations directly from atomic coordinates. Tested on three benchmark systems, our approach predicts essential structural, thermodynamic and kinetic information for slow processes, demonstrating robustness across diverse systems. The method shows promise for complex systems, enabling effective enhanced sampling without requiring pre-defined reaction coordinates or input features.
{"title":"Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) approach for learning molecular thermodynamics and kinetics","authors":"Ziyue Zou, Dedi Wang, Pratyush Tiwary","doi":"arxiv-2409.11843","DOIUrl":"https://doi.org/arxiv-2409.11843","url":null,"abstract":"Molecular dynamics simulations offer detailed insights into atomic motions\u0000but face timescale limitations. Enhanced sampling methods have addressed these\u0000challenges but even with machine learning, they often rely on pre-selected\u0000expert-based features. In this work, we present the Graph Neural Network-State\u0000Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph\u0000neural networks and the State Predictive Information Bottleneck to\u0000automatically learn low-dimensional representations directly from atomic\u0000coordinates. Tested on three benchmark systems, our approach predicts essential\u0000structural, thermodynamic and kinetic information for slow processes,\u0000demonstrating robustness across diverse systems. The method shows promise for\u0000complex systems, enabling effective enhanced sampling without requiring\u0000pre-defined reaction coordinates or input features.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mingyuan Zheng, Dmytro Khomenko, Patrick Charbonneau
Simple active models of matter recapitulate complex biological phenomena. Their out-of-equilibrium nature, however, often makes these models beyond the reach of first-principle descriptions. This limitation is particularly perplexing when attempting to distinguish between different glass-forming mechanisms. We here consider a minimal active system in various spatial dimensions to identify the underlying processes at play. Activity is found to markedly impact cage escape processes and critical fluctuations, thus offering a distinct perspective on the role of activity sluggish dynamics.
{"title":"Not-so-glass-like Caging and Fluctuations of an Active Matter Model","authors":"Mingyuan Zheng, Dmytro Khomenko, Patrick Charbonneau","doi":"arxiv-2409.12037","DOIUrl":"https://doi.org/arxiv-2409.12037","url":null,"abstract":"Simple active models of matter recapitulate complex biological phenomena.\u0000Their out-of-equilibrium nature, however, often makes these models beyond the\u0000reach of first-principle descriptions. This limitation is particularly\u0000perplexing when attempting to distinguish between different glass-forming\u0000mechanisms. We here consider a minimal active system in various spatial\u0000dimensions to identify the underlying processes at play. Activity is found to\u0000markedly impact cage escape processes and critical fluctuations, thus offering\u0000a distinct perspective on the role of activity sluggish dynamics.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Giuliano G. Porciúncula, Marcone I. Sena Júnior, Luiz Felipe C. Pereira, André L. M. Vilela
Online platforms for social interactions are an essential part of modern society. With the advance of technology and the rise of algorithms and AI, content is now filtered systematically and facilitates the formation of filter bubbles. This work investigates the social consensus under limited visibility in a two-state majority-vote model on Barab'asi-Albert scale-free networks. In the consensus evolution, each individual assimilates the opinion of the majority of their neighbors with probability $1-q$ and disagrees with chance $q$, known as the noise parameter. We define the visibility parameter $V$ as the probability of an individual considering the opinion of a neighbor at a given interaction. The parameter $V$ enables us to model the limited visibility phenomenon that produces synthetic neighborhoods in online interactions. We employ Monte Carlo simulations and finite-size scaling analysis to obtain the critical noise parameter as a function of the visibility $V$ and the growth parameter $z$. We find the critical exponents $beta/bar{nu}$, $gamma/bar{nu}$ and $1/bar{nu}$ of and validate their unitary relation for complex networks. Our analysis shows that installing and manipulating synthetic influence groups critically undermines consensus robustness.
{"title":"Consensus effects of social media synthetic influence groups on scale-free networks","authors":"Giuliano G. Porciúncula, Marcone I. Sena Júnior, Luiz Felipe C. Pereira, André L. M. Vilela","doi":"arxiv-2409.10830","DOIUrl":"https://doi.org/arxiv-2409.10830","url":null,"abstract":"Online platforms for social interactions are an essential part of modern\u0000society. With the advance of technology and the rise of algorithms and AI,\u0000content is now filtered systematically and facilitates the formation of filter\u0000bubbles. This work investigates the social consensus under limited visibility\u0000in a two-state majority-vote model on Barab'asi-Albert scale-free networks. In\u0000the consensus evolution, each individual assimilates the opinion of the\u0000majority of their neighbors with probability $1-q$ and disagrees with chance\u0000$q$, known as the noise parameter. We define the visibility parameter $V$ as\u0000the probability of an individual considering the opinion of a neighbor at a\u0000given interaction. The parameter $V$ enables us to model the limited visibility\u0000phenomenon that produces synthetic neighborhoods in online interactions. We\u0000employ Monte Carlo simulations and finite-size scaling analysis to obtain the\u0000critical noise parameter as a function of the visibility $V$ and the growth\u0000parameter $z$. We find the critical exponents $beta/bar{nu}$,\u0000$gamma/bar{nu}$ and $1/bar{nu}$ of and validate their unitary relation for\u0000complex networks. Our analysis shows that installing and manipulating synthetic\u0000influence groups critically undermines consensus robustness.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The mechanical response of amorphous solids to external strains is riddled with plastic events that create topological charges in the resulting displacement field. It was recently shown that the latter leads to screening phenomena that are accompanied by the breaking of both translational and Chiral symmetries. The screening effects are quantified by two screening parameters $kappa_e$ and $kappa_o$, which are inverse characteristic lengths that do not exist in classical elasticity. The screening parameters (and the associated lengths) are emergent, and it is important to understand how they are selected. This Letter explores the mechanism of selection of these characteristic lengths in two examples of strain protocols that allow analytic scrutiny.
{"title":"Selection Principle for the Screening Parameters in the Mechanical Response of Amorphous Solids","authors":"Pawandeep Kaur, Itamar Procaccia, Tuhin Samanta","doi":"arxiv-2409.11507","DOIUrl":"https://doi.org/arxiv-2409.11507","url":null,"abstract":"The mechanical response of amorphous solids to external strains is riddled\u0000with plastic events that create topological charges in the resulting\u0000displacement field. It was recently shown that the latter leads to screening\u0000phenomena that are accompanied by the breaking of both translational and Chiral\u0000symmetries. The screening effects are quantified by two screening parameters\u0000$kappa_e$ and $kappa_o$, which are inverse characteristic lengths that do not\u0000exist in classical elasticity. The screening parameters (and the associated\u0000lengths) are emergent, and it is important to understand how they are selected.\u0000This Letter explores the mechanism of selection of these characteristic lengths\u0000in two examples of strain protocols that allow analytic scrutiny.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"112 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Motivated by the fractal form of the compact chromatin in vivo, we study the melting of a lattice DNA on the infinite cluster backbone near the three-dimensional site percolation critical point $(p_c=0.3116)$, which exhibits fractal-like properties, using Monte Carlo simulations. Further, we extend our study to other values of atmospheric disorder $(p_cleq p leq 1)$ and show how the melting temperature varies with a decrease in the availability of lattice sites mimicking the crowded environment inside the cell nucleus. Importantly, we found that the melting transition sharpens with a linear increase in the denaturation temperature as we increase the degree of disorder. Two separate disorder regimes showing weak and strong effects on melting can be identified. For simulations, we use the pruned and enriched Rosenbluth method in conjunction with a depth-first implementation of the Leath algorithm to generate the underlying disorder.
{"title":"Influence of media disorder on DNA melting","authors":"Debjyoti Majumdar","doi":"arxiv-2409.11030","DOIUrl":"https://doi.org/arxiv-2409.11030","url":null,"abstract":"Motivated by the fractal form of the compact chromatin in vivo, we study the\u0000melting of a lattice DNA on the infinite cluster backbone near the\u0000three-dimensional site percolation critical point $(p_c=0.3116)$, which\u0000exhibits fractal-like properties, using Monte Carlo simulations. Further, we\u0000extend our study to other values of atmospheric disorder $(p_cleq p leq 1)$\u0000and show how the melting temperature varies with a decrease in the availability\u0000of lattice sites mimicking the crowded environment inside the cell nucleus.\u0000Importantly, we found that the melting transition sharpens with a linear\u0000increase in the denaturation temperature as we increase the degree of disorder.\u0000Two separate disorder regimes showing weak and strong effects on melting can be\u0000identified. For simulations, we use the pruned and enriched Rosenbluth method\u0000in conjunction with a depth-first implementation of the Leath algorithm to\u0000generate the underlying disorder.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Sarkanych, Yu. Sevinchan, M. Krasnytska, P. Romanczuk, Yu. Holovatch
In this paper we investigate a model of consensus decision making [Hartnett A. T., et al., Phys. Rev. Lett., 2016, 116, 038701] following a statistical physics approach presented in [Sarkanych P., et al., Phys. Biol., 2023, 20, 045005]. Within this approach, the temperature serves as a measure of fluctuations, not considered before in the original model. Here, we discuss the model on a complete graph. The main goal of this paper is to show that an analytical description may lead to a very rich phase behaviour, which is usually not expected for a complete graph. However, the variety of individual agent (spin) features - their inhomogeneity and bias strength - taken into account by the model leads to rather non-trivial collective effects. We show that the latter may emerge in a form of continuous or abrupt phase transitions sometimes accompanied by re-entrant and order-parameter flipping behaviour. In turn, this may lead to appealing interpretations in terms of social decision making. We support analytical predictions by numerical simulation. Moreover, while analytical calculations are performed within an equilibrium statistical physics formalism, the numerical simulations add yet another dynamical feature - local non-linearity or conformity of the individual to the opinion of its surroundings. This feature appears to have a strong impact both on the way in which an equilibrium state is approached as well as on its characteristics.
在本文中，我们按照[Sarkanych P. 等，Phys. Biol., 2023, 20,045005]中提出的统计物理学方法，研究了一个共识决策模型[HartnettA. T. 等，Phys. Rev. Lett., 2016, 116, 038701]。在这一方法中，温度被用作波动的度量，而这在最初的模型中是没有考虑到的。在此，我们讨论完整图上的模型。本文的主要目的是说明分析描述可能导致非常丰富的相位行为，而这通常是完整图所不具备的。然而，模型所考虑到的各种单体（自旋）特征--它们的不均匀性和偏置强度--导致了相当非同小可的集体效应。我们证明，后者可能以连续或突然相变的形式出现，有时还伴随着再中心和阶参数翻转行为。反过来，这可能会导致从社会决策的角度进行有吸引力的解释。我们通过数值模拟来支持分析预测。此外，虽然分析计算是在平衡统计物理学形式中进行的，但数值模拟增加了另一个动力学特征--局部非线性或个体对周围意见的顺从。这一特征似乎对接近平衡态的方式及其特征都有很大影响。
{"title":"Consensus decision making on a complete graph: complex behaviour from simple assumptions","authors":"P. Sarkanych, Yu. Sevinchan, M. Krasnytska, P. Romanczuk, Yu. Holovatch","doi":"arxiv-2409.11475","DOIUrl":"https://doi.org/arxiv-2409.11475","url":null,"abstract":"In this paper we investigate a model of consensus decision making [Hartnett\u0000A. T., et al., Phys. Rev. Lett., 2016, 116, 038701] following a statistical\u0000physics approach presented in [Sarkanych P., et al., Phys. Biol., 2023, 20,\u0000045005]. Within this approach, the temperature serves as a measure of\u0000fluctuations, not considered before in the original model. Here, we discuss the\u0000model on a complete graph. The main goal of this paper is to show that an\u0000analytical description may lead to a very rich phase behaviour, which is\u0000usually not expected for a complete graph. However, the variety of individual\u0000agent (spin) features - their inhomogeneity and bias strength - taken into\u0000account by the model leads to rather non-trivial collective effects. We show\u0000that the latter may emerge in a form of continuous or abrupt phase transitions\u0000sometimes accompanied by re-entrant and order-parameter flipping behaviour. In\u0000turn, this may lead to appealing interpretations in terms of social decision\u0000making. We support analytical predictions by numerical simulation. Moreover,\u0000while analytical calculations are performed within an equilibrium statistical\u0000physics formalism, the numerical simulations add yet another dynamical feature\u0000- local non-linearity or conformity of the individual to the opinion of its\u0000surroundings. This feature appears to have a strong impact both on the way in\u0000which an equilibrium state is approached as well as on its characteristics.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142268518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in their strength was suggested [Krasnytska et al., J. Phys. Complex., 2020, 1, 035008]. The model was analyzed for a particular case when agents are located on sites of a scale-free network and agent strength is a random variable governed by a power-law decaying distribution. For the annealed network, the exact solution shows a rich phase diagram with different types of critical behavior and new universality classes. This paper continues the above studies and addresses the analysis of scaling functions and universal critical amplitude ratios for the model on a scale-free network.
{"title":"Ising model with varying spin strength on a scale-free network: scaling functions and critical amplitude ratios","authors":"M. Krasnytska","doi":"arxiv-2409.11396","DOIUrl":"https://doi.org/arxiv-2409.11396","url":null,"abstract":"Recently, a novel model to describe ordering in systems comprising agents\u0000which, although matching in their binarity (i.e., maintaining the iconic Ising\u0000features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still\u0000differing in their strength was suggested [Krasnytska et al., J. Phys.\u0000Complex., 2020, 1, 035008]. The model was analyzed for a particular case when\u0000agents are located on sites of a scale-free network and agent strength is a\u0000random variable governed by a power-law decaying distribution. For the annealed\u0000network, the exact solution shows a rich phase diagram with different types of\u0000critical behavior and new universality classes. This paper continues the above\u0000studies and addresses the analysis of scaling functions and universal critical\u0000amplitude ratios for the model on a scale-free network.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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