Recently observed scaling in the random-anisotropy model of amorphous or sintered ferromagnets is derived by an alternative method and extended for studying the dynamical properties in terms of the Landau-Lifshitz equations for spin blocks. Switching to the rescaled exchange and anisotropy constants allows one to investigate the dynamics by using a reduced number of variables, which greatly speeds up computations. The proposed dynamical scaling is applied to the problem of microwave absorption by a random anisotropy magnet. The equivalence of the rescaled model to the original atomic model is confirmed numerically. The method is proposed as a powerful tool in studying static and dynamic properties of systems with quenched randomness.
{"title":"Scaling of Static and Dynamical Properties of Random Anisotropy Magnets","authors":"Dmitry A. Garanin, Eugene M. Chudnovsky","doi":"arxiv-2407.21520","DOIUrl":"https://doi.org/arxiv-2407.21520","url":null,"abstract":"Recently observed scaling in the random-anisotropy model of amorphous or\u0000sintered ferromagnets is derived by an alternative method and extended for\u0000studying the dynamical properties in terms of the Landau-Lifshitz equations for\u0000spin blocks. Switching to the rescaled exchange and anisotropy constants allows\u0000one to investigate the dynamics by using a reduced number of variables, which\u0000greatly speeds up computations. The proposed dynamical scaling is applied to\u0000the problem of microwave absorption by a random anisotropy magnet. The\u0000equivalence of the rescaled model to the original atomic model is confirmed\u0000numerically. The method is proposed as a powerful tool in studying static and\u0000dynamic properties of systems with quenched randomness.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886204","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}
Obtaining the low-energy configurations of spin glasses that have rugged energy landscapes is of direct relevance to combinatorial optimization and fundamental science. Search-based heuristics have difficulty with this task due to the existence of many local minima that are far from optimal. The work of [M. M. Rams et al., Phys. Rev. E 104, 025308 (2021)] demonstrates an alternative that can bypass this issue for spin glasses with planar or quasi-planar geometry: sampling the Boltzmann distribution via approximate contractions of tensor networks. The computational complexity of this approach is due only to the complexity of contracting the network, and is therefore independent of landscape ruggedness. Here we initiate an investigation of how to take this approach beyond (quasi-)planar geometry by utilizing hyperoptimized approximate contraction of tensor networks [J. Gray and G. K.-L. Chan, Phys. Rev. X 14, 011009 (2024)]. We perform tests on the periodic square- and cubic-lattice, planted-solution Ising spin glasses generated with tile planting [F. Hamze et al., Phys. Rev. E 97, 043303 (2018)] for up to 2304 (square lattice) and 216 (cubic lattice) spins. For a fixed bond dimension, the time complexity is quadratic. With a bond dimension of only four, over the tested system sizes the average solution quality in the most rugged instance class remains at ~1% (square lattice) or ~10% (cubic lattice) of optimal. These results encourage further investigation of tensor network contraction for rugged-energy-landscape spin-glass problems, especially given that this approach is not limited to the Ising (i.e., binary) or two-body (i.e., quadratic) settings.
获得具有崎岖能量景观的自旋玻璃低能构型与组合优化和基础科学直接相关。基于搜索的启发式方法很难完成这项任务，因为存在许多远非最优的局部极小值。M. M. Rams 等人，Phys. Rev. E 104, 025308 (2021)]的研究表明，对于具有平面或准平面几何形状的自旋玻璃来说，有一种替代方法可以绕过这个问题：通过张量网络的近似收缩对玻尔兹曼分布进行采样。这种方法的计算复杂性仅仅是由于收缩网络的复杂性造成的，因此与地形的凹凸无关。在这里，我们开始研究如何利用张量网络的近似收缩进行超优化，从而使这种方法超越（准）平面几何[J. Gray and G. K.-L.Chan, Phys. Rev. X 14, 011009 (2024)]。我们对用瓦片种植法生成的周期性方形和立方晶格、种植溶液伊辛自旋玻璃进行了测试[F. Hamze 等，Phys. Rev. E 97, 043303 (2018)]，最多可处理 2304 个（方形晶格）和 216 个（立方晶格）自旋。对于固定的键维度，时间复杂度是二次方。在键维仅为四的情况下，在测试的系统大小中，最崎岖实例类的平均解质量保持在最优解的 ~1% （方晶格）或 ~10% （立方晶格）。这些结果鼓励我们进一步研究张量网络收缩对崎岖能谱自旋玻璃问题的影响，特别是考虑到这种方法并不局限于伊辛（即二元）或二体（即四元）设置。
{"title":"Hyperoptimized approximate contraction of tensor networks for rugged-energy-landscape spin glasses on periodic square and cubic lattices","authors":"Adil A. Gangat, Johnnie Gray","doi":"arxiv-2407.21287","DOIUrl":"https://doi.org/arxiv-2407.21287","url":null,"abstract":"Obtaining the low-energy configurations of spin glasses that have rugged\u0000energy landscapes is of direct relevance to combinatorial optimization and\u0000fundamental science. Search-based heuristics have difficulty with this task due\u0000to the existence of many local minima that are far from optimal. The work of\u0000[M. M. Rams et al., Phys. Rev. E 104, 025308 (2021)] demonstrates an\u0000alternative that can bypass this issue for spin glasses with planar or\u0000quasi-planar geometry: sampling the Boltzmann distribution via approximate\u0000contractions of tensor networks. The computational complexity of this approach\u0000is due only to the complexity of contracting the network, and is therefore\u0000independent of landscape ruggedness. Here we initiate an investigation of how\u0000to take this approach beyond (quasi-)planar geometry by utilizing\u0000hyperoptimized approximate contraction of tensor networks [J. Gray and G. K.-L.\u0000Chan, Phys. Rev. X 14, 011009 (2024)]. We perform tests on the periodic square-\u0000and cubic-lattice, planted-solution Ising spin glasses generated with tile\u0000planting [F. Hamze et al., Phys. Rev. E 97, 043303 (2018)] for up to 2304\u0000(square lattice) and 216 (cubic lattice) spins. For a fixed bond dimension, the\u0000time complexity is quadratic. With a bond dimension of only four, over the\u0000tested system sizes the average solution quality in the most rugged instance\u0000class remains at ~1% (square lattice) or ~10% (cubic lattice) of optimal. These\u0000results encourage further investigation of tensor network contraction for\u0000rugged-energy-landscape spin-glass problems, especially given that this\u0000approach is not limited to the Ising (i.e., binary) or two-body (i.e.,\u0000quadratic) settings.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886238","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}
Hao Liao, Wei Zhang, Zhanyi Huang, Zexiao Long, Mingyang Zhou, Xiaoqun Wu, Rui Mao, Chi Ho Yeung
In the past decade, significant strides in deep learning have led to numerous groundbreaking applications. Despite these advancements, the understanding of the high generalizability of deep learning, especially in such an over-parametrized space, remains limited. Successful applications are often considered as empirical rather than scientific achievements. For instance, deep neural networks' (DNNs) internal representations, decision-making mechanism, absence of overfitting in an over-parametrized space, high generalizability, etc., remain less understood. This paper delves into the loss landscape of DNNs through the lens of spin glass in statistical physics, i.e. a system characterized by a complex energy landscape with numerous metastable states, to better understand how DNNs work. We investigated a single hidden layer Rectified Linear Unit (ReLU) neural network model, and introduced several protocols to examine the analogy between DNNs (trained with datasets including MNIST and CIFAR10) and spin glass. Specifically, we used (1) random walk in the parameter space of DNNs to unravel the structures in their loss landscape; (2) a permutation-interpolation protocol to study the connection between copies of identical regions in the loss landscape due to the permutation symmetry in the hidden layers; (3) hierarchical clustering to reveal the hierarchy among trained solutions of DNNs, reminiscent of the so-called Replica Symmetry Breaking (RSB) phenomenon (i.e. the Parisi solution) in analogy to spin glass; (4) finally, we examine the relationship between the degree of the ruggedness of the loss landscape of the DNN and its generalizability, showing an improvement of flattened minima.
{"title":"Exploring Loss Landscapes through the Lens of Spin Glass Theory","authors":"Hao Liao, Wei Zhang, Zhanyi Huang, Zexiao Long, Mingyang Zhou, Xiaoqun Wu, Rui Mao, Chi Ho Yeung","doi":"arxiv-2407.20724","DOIUrl":"https://doi.org/arxiv-2407.20724","url":null,"abstract":"In the past decade, significant strides in deep learning have led to numerous\u0000groundbreaking applications. Despite these advancements, the understanding of\u0000the high generalizability of deep learning, especially in such an\u0000over-parametrized space, remains limited. Successful applications are often\u0000considered as empirical rather than scientific achievements. For instance, deep\u0000neural networks' (DNNs) internal representations, decision-making mechanism,\u0000absence of overfitting in an over-parametrized space, high generalizability,\u0000etc., remain less understood. This paper delves into the loss landscape of DNNs\u0000through the lens of spin glass in statistical physics, i.e. a system\u0000characterized by a complex energy landscape with numerous metastable states, to\u0000better understand how DNNs work. We investigated a single hidden layer\u0000Rectified Linear Unit (ReLU) neural network model, and introduced several\u0000protocols to examine the analogy between DNNs (trained with datasets including\u0000MNIST and CIFAR10) and spin glass. Specifically, we used (1) random walk in the\u0000parameter space of DNNs to unravel the structures in their loss landscape; (2)\u0000a permutation-interpolation protocol to study the connection between copies of\u0000identical regions in the loss landscape due to the permutation symmetry in the\u0000hidden layers; (3) hierarchical clustering to reveal the hierarchy among\u0000trained solutions of DNNs, reminiscent of the so-called Replica Symmetry\u0000Breaking (RSB) phenomenon (i.e. the Parisi solution) in analogy to spin glass;\u0000(4) finally, we examine the relationship between the degree of the ruggedness\u0000of the loss landscape of the DNN and its generalizability, showing an\u0000improvement of flattened minima.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141862638","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}
Christoph S. Setescak, Caio Lewenkopf, Matthias Ludewig
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the bulk-boundary correspondence, reproduces physical knowledge, and leads to an efficient and tractable numerical approach for calculating invariants. As a showcase, we give a detailed discussion of the framework for three-dimensional systems with time-reversal symmetry. We numerically reproduce the known disorder-free phase diagram of a tunable, effective tight-binding model and analyze the evolution of the topological phase under disorder.
{"title":"Coarse geometric approach to topological phases: Invariants from real-space representations","authors":"Christoph S. Setescak, Caio Lewenkopf, Matthias Ludewig","doi":"arxiv-2407.16494","DOIUrl":"https://doi.org/arxiv-2407.16494","url":null,"abstract":"We show that topological phases include disordered materials if the\u0000underlying invariant is interpreted as originating from coarse geometry. This\u0000coarse geometric framework, grounded in physical principles, offers a natural\u0000setting for the bulk-boundary correspondence, reproduces physical knowledge,\u0000and leads to an efficient and tractable numerical approach for calculating\u0000invariants. As a showcase, we give a detailed discussion of the framework for\u0000three-dimensional systems with time-reversal symmetry. We numerically reproduce\u0000the known disorder-free phase diagram of a tunable, effective tight-binding\u0000model and analyze the evolution of the topological phase under disorder.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784223","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}
Here we outline some new results for the GHWS model which points to a discretization of parameter space into well differentiated collective dynamic states. We argue this can lead to basic processes in parameter space, starting with minimum modelling ingredients: a complex network with a disorder parameter and an excitable dynamics (cellular automata) on it.
{"title":"Some new results for the GHWS model","authors":"Leonardo Reyes","doi":"arxiv-2407.14318","DOIUrl":"https://doi.org/arxiv-2407.14318","url":null,"abstract":"Here we outline some new results for the GHWS model which points to a\u0000discretization of parameter space into well differentiated collective dynamic\u0000states. We argue this can lead to basic processes in parameter space, starting\u0000with minimum modelling ingredients: a complex network with a disorder parameter\u0000and an excitable dynamics (cellular automata) on it.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744133","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}
Localization phenomenon is an important research field in condensed matter physics. However, due to the complexity and subtlety of disordered syestems, new localization phenomena always emerge unexpectedly. For example, it is generally believed that the phase of the hopping term does not affect the localization properties of the system, so the calculation of the phase is often ignored in the study of localization. Here, we introduce a quasiperiodic model and demonstrate that the phase change of the hopping term can significantly alter the localization properties of the system through detailed numerical simulations such as the inverse participation ratio and multifractal analysis. This phase-induced localization transition provides valuable information for the study of localization physics.
{"title":"Phase induced localization transition","authors":"Tong Liu, Xingbo Wei, Youguo Wang","doi":"arxiv-2407.10043","DOIUrl":"https://doi.org/arxiv-2407.10043","url":null,"abstract":"Localization phenomenon is an important research field in condensed matter\u0000physics. However, due to the complexity and subtlety of disordered syestems,\u0000new localization phenomena always emerge unexpectedly. For example, it is\u0000generally believed that the phase of the hopping term does not affect the\u0000localization properties of the system, so the calculation of the phase is often\u0000ignored in the study of localization. Here, we introduce a quasiperiodic model\u0000and demonstrate that the phase change of the hopping term can significantly\u0000alter the localization properties of the system through detailed numerical\u0000simulations such as the inverse participation ratio and multifractal analysis.\u0000This phase-induced localization transition provides valuable information for\u0000the study of localization physics.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720399","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}
Bo Zhou, Xingsong Feng, Xianmin Guo, Fei Gao, Hongsheng Chen, Zuojia Wang
In this letter, we investigate the statistical properties of electromagnetic signals after different times of duration within one-dimensional local-disordered time-varying cavities, where both spatial and temporal disorders are added. Our findings reveal that, in the vast majority of cases, adequate temporal disorder in local space can make the electromagnetic field statistically localized, obeying a normal distribution at a specific point in time of arbitrary location within the cavity. We employ the concept of disordered space-time crystals and leverage Lindeberg's and Lyapunov's theorems to theoretically prove the normal distribution of the field values. Furthermore, we find that with the increase of energy provided by time variation, the probability of extreme fields will significantly increase and the field intensity eventually is de-normalized, that is, deviating from the normal distribution. This study not only sheds light on the statistical properties of transient signals in local-disordered time-varying systems but also paves the way for further exploration in wave dynamics of analogous systems.
{"title":"Statistical Localization of Electromagnetic Signals in Disordered Time-Varying Cavity","authors":"Bo Zhou, Xingsong Feng, Xianmin Guo, Fei Gao, Hongsheng Chen, Zuojia Wang","doi":"arxiv-2407.21023","DOIUrl":"https://doi.org/arxiv-2407.21023","url":null,"abstract":"In this letter, we investigate the statistical properties of electromagnetic\u0000signals after different times of duration within one-dimensional\u0000local-disordered time-varying cavities, where both spatial and temporal\u0000disorders are added. Our findings reveal that, in the vast majority of cases,\u0000adequate temporal disorder in local space can make the electromagnetic field\u0000statistically localized, obeying a normal distribution at a specific point in\u0000time of arbitrary location within the cavity. We employ the concept of\u0000disordered space-time crystals and leverage Lindeberg's and Lyapunov's theorems\u0000to theoretically prove the normal distribution of the field values.\u0000Furthermore, we find that with the increase of energy provided by time\u0000variation, the probability of extreme fields will significantly increase and\u0000the field intensity eventually is de-normalized, that is, deviating from the\u0000normal distribution. This study not only sheds light on the statistical\u0000properties of transient signals in local-disordered time-varying systems but\u0000also paves the way for further exploration in wave dynamics of analogous\u0000systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886239","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}
Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras, Symeon I. Tsintzos
Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising Machines have proven to be advantageous for simulating fully connected large-scale spin systems. However, fine control of a general interaction matrix $J$ has so far only been accomplished through eigenvalue decomposition methods that either limit the scalability or increase the execution time of the optimization process. We introduce and experimentally validate a SPIM instance that enables direct control over the full interaction matrix, enabling the encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We demonstrate the conformity of the experimentally measured Ising energy with the theoretically expected values and then proceed to solve both the unweighted and weighted graph partitioning problems, showcasing a systematic convergence to an optimal solution via simulated annealing. Our approach greatly expands the applicability of SPIMs for real-world applications without sacrificing any of the inherent advantages of the system, and paves the way to encoding the full range of NP problems that are known to be equivalent to Ising models, on SPIM devices.
{"title":"Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines","authors":"Jason Sakellariou, Alexis Askitopoulos, Georgios Pastras, Symeon I. Tsintzos","doi":"arxiv-2407.09161","DOIUrl":"https://doi.org/arxiv-2407.09161","url":null,"abstract":"Photonic Ising Machines constitute an emergent new paradigm of computation,\u0000geared towards tackling combinatorial optimization problems that can be reduced\u0000to the problem of finding the ground state of an Ising model. Spatial Photonic\u0000Ising Machines have proven to be advantageous for simulating fully connected\u0000large-scale spin systems. However, fine control of a general interaction matrix\u0000$J$ has so far only been accomplished through eigenvalue decomposition methods\u0000that either limit the scalability or increase the execution time of the\u0000optimization process. We introduce and experimentally validate a SPIM instance\u0000that enables direct control over the full interaction matrix, enabling the\u0000encoding of Ising Hamiltonians with arbitrary couplings and connectivity. We\u0000demonstrate the conformity of the experimentally measured Ising energy with the\u0000theoretically expected values and then proceed to solve both the unweighted and\u0000weighted graph partitioning problems, showcasing a systematic convergence to an\u0000optimal solution via simulated annealing. Our approach greatly expands the\u0000applicability of SPIMs for real-world applications without sacrificing any of\u0000the inherent advantages of the system, and paves the way to encoding the full\u0000range of NP problems that are known to be equivalent to Ising models, on SPIM\u0000devices.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720400","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}
Diffusion-based generative models are machine learning models that use diffusion processes to learn the probability distribution of high-dimensional data. In recent years, they have become extremely successful in generating multimedia content. However, it is still unknown if such models can be used to generate high-quality datasets of physical models. In this work, we use a Landau-Ginzburg-like diffusion model to infer the distribution of a $2D$ bond-diluted Ising model. Our approach is simple and effective, and we show that the generated samples reproduce correctly the statistical and critical properties of the physical model.
{"title":"A Very Effective and Simple Diffusion Reconstruction for the Diluted Ising Model","authors":"Stefano Bae, Enzo Marinari, Federico Ricci-Tersenghi","doi":"arxiv-2407.07266","DOIUrl":"https://doi.org/arxiv-2407.07266","url":null,"abstract":"Diffusion-based generative models are machine learning models that use\u0000diffusion processes to learn the probability distribution of high-dimensional\u0000data. In recent years, they have become extremely successful in generating\u0000multimedia content. However, it is still unknown if such models can be used to\u0000generate high-quality datasets of physical models. In this work, we use a\u0000Landau-Ginzburg-like diffusion model to infer the distribution of a $2D$\u0000bond-diluted Ising model. Our approach is simple and effective, and we show\u0000that the generated samples reproduce correctly the statistical and critical\u0000properties of the physical model.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141586773","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}
Replica Symmetry Breaking is a fascinating phenomenon of spin glasses model which could have consequences also in other field of studies. Although there are several studies regarding the stability between the Replica Symmetric and first step of Replica Symmetry Breaking approximations, we do not have results for the following steps (apart from that one by Gardner for P-spin glasses in 1985). This is link to the fact that the classic method, based from the work by De Almeida and Thoules (from which the critical stability line takes its name), is difficult to be generalise for the next assumptions. In this paper we devise a new straightforward method inspired to the work by Toninelli in 2002 to recover the critical line in order to inspect the stability between the second step of Replica Symmetry Breaking and the first one. Moreover, we generalise to Kth step, with K finite.
复制对称性破坏是自旋玻璃模型的一个迷人现象，它也可能对其他研究领域产生影响。虽然有一些关于复制对称和复制对称破缺近似第一步之间稳定性的研究，但我们还没有关于后续步骤的结果（除了加德纳在 1985 年针对 P 自旋玻璃所做的研究）。这是因为基于 De Almeida 和 Thoules 工作的经典方法（临界稳定线的名称即来源于此）很难推广到下一步假设。本文受托尼内利 2002 年工作的启发，设计了一种新的直接方法来恢复临界线，以检验复制对称破缺第二步与第一步之间的稳定性。此外，我们还将其推广到 K 有限的第 K 步。
{"title":"About the AT line in Replica Symmetry Breaking assumption for spin glasses","authors":"Linda Albanese","doi":"arxiv-2407.06701","DOIUrl":"https://doi.org/arxiv-2407.06701","url":null,"abstract":"Replica Symmetry Breaking is a fascinating phenomenon of spin glasses model\u0000which could have consequences also in other field of studies. Although there\u0000are several studies regarding the stability between the Replica Symmetric and\u0000first step of Replica Symmetry Breaking approximations, we do not have results\u0000for the following steps (apart from that one by Gardner for P-spin glasses in\u00001985). This is link to the fact that the classic method, based from the work by\u0000De Almeida and Thoules (from which the critical stability line takes its name),\u0000is difficult to be generalise for the next assumptions. In this paper we devise\u0000a new straightforward method inspired to the work by Toninelli in 2002 to\u0000recover the critical line in order to inspect the stability between the second\u0000step of Replica Symmetry Breaking and the first one. Moreover, we generalise to\u0000Kth step, with K finite.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141569172","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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