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Scaling of Static and Dynamical Properties of Random Anisotropy Magnets 随机各向异性磁体的静态和动态特性缩放
Pub Date : 2024-07-31 DOI: arxiv-2407.21520
Dmitry A. Garanin, Eugene M. Chudnovsky
Recently observed scaling in the random-anisotropy model of amorphous orsintered ferromagnets is derived by an alternative method and extended forstudying the dynamical properties in terms of the Landau-Lifshitz equations forspin blocks. Switching to the rescaled exchange and anisotropy constants allowsone to investigate the dynamics by using a reduced number of variables, whichgreatly speeds up computations. The proposed dynamical scaling is applied tothe problem of microwave absorption by a random anisotropy magnet. Theequivalence of the rescaled model to the original atomic model is confirmednumerically. The method is proposed as a powerful tool in studying static anddynamic properties of systems with quenched randomness.
最近在非晶或烧结铁磁体的随机各向异性模型中观察到的缩放现象是通过另一种方法推导出来的,并扩展到了用自旋块的朗道-利夫希茨方程来研究动力学特性。改用重标度交换常数和各向异性常数可以减少变量数量,从而大大加快计算速度。我们将所提出的动力学比例应用于随机各向异性磁体的微波吸收问题。用数值方法证实了重构模型与原始原子模型的等效性。该方法是研究具有淬火随机性的系统的静态和动态特性的有力工具。
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引用次数: 0
Hyperoptimized approximate contraction of tensor networks for rugged-energy-landscape spin glasses on periodic square and cubic lattices 周期性方形和立方晶格上崎岖能谱自旋玻璃张量网络的超优化近似收缩
Pub Date : 2024-07-31 DOI: arxiv-2407.21287
Adil A. Gangat, Johnnie Gray
Obtaining the low-energy configurations of spin glasses that have ruggedenergy landscapes is of direct relevance to combinatorial optimization andfundamental science. Search-based heuristics have difficulty with this task dueto 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 analternative that can bypass this issue for spin glasses with planar orquasi-planar geometry: sampling the Boltzmann distribution via approximatecontractions of tensor networks. The computational complexity of this approachis due only to the complexity of contracting the network, and is thereforeindependent of landscape ruggedness. Here we initiate an investigation of howto take this approach beyond (quasi-)planar geometry by utilizinghyperoptimized 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 tileplanting [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, thetime complexity is quadratic. With a bond dimension of only four, over thetested system sizes the average solution quality in the most rugged instanceclass remains at ~1% (square lattice) or ~10% (cubic lattice) of optimal. Theseresults encourage further investigation of tensor network contraction forrugged-energy-landscape spin-glass problems, especially given that thisapproach 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。
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引用次数: 0
Exploring Loss Landscapes through the Lens of Spin Glass Theory 通过旋转玻璃理论探索损失景观
Pub Date : 2024-07-30 DOI: arxiv-2407.20724
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 numerousgroundbreaking applications. Despite these advancements, the understanding ofthe high generalizability of deep learning, especially in such anover-parametrized space, remains limited. Successful applications are oftenconsidered as empirical rather than scientific achievements. For instance, deepneural 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 DNNsthrough the lens of spin glass in statistical physics, i.e. a systemcharacterized by a complex energy landscape with numerous metastable states, tobetter understand how DNNs work. We investigated a single hidden layerRectified Linear Unit (ReLU) neural network model, and introduced severalprotocols to examine the analogy between DNNs (trained with datasets includingMNIST and CIFAR10) and spin glass. Specifically, we used (1) random walk in theparameter space of DNNs to unravel the structures in their loss landscape; (2)a permutation-interpolation protocol to study the connection between copies ofidentical regions in the loss landscape due to the permutation symmetry in thehidden layers; (3) hierarchical clustering to reveal the hierarchy amongtrained solutions of DNNs, reminiscent of the so-called Replica SymmetryBreaking (RSB) phenomenon (i.e. the Parisi solution) in analogy to spin glass;(4) finally, we examine the relationship between the degree of the ruggednessof the loss landscape of the DNN and its generalizability, showing animprovement of flattened minima.
在过去十年中,深度学习取得了长足进步,产生了众多突破性应用。尽管取得了这些进步,但人们对深度学习的高通用性的理解仍然有限,尤其是在这样一个过度参数化的空间。成功的应用通常被视为经验成就而非科学成就。例如,人们对深度神经网络(DNN)的内部表征、决策机制、在过度参数化的空间中不存在过拟合、高泛化能力等方面的了解仍然较少。为了更好地理解 DNNs 的工作原理,本文通过统计物理学中的自旋玻璃透镜来深入研究 DNNs 的损耗图景,即一个具有复杂能量图景和众多可变状态的系统。我们研究了单隐层整齐线性单元(ReLU)神经网络模型,并引入了几种协议来检验 DNN(使用包括 MNIST 和 CIFAR10 在内的数据集进行训练)与自旋玻璃之间的类比关系。具体来说,我们使用(1)在 DNN 的参数空间中随机行走来揭示其损失景观中的结构;(2)使用 permutation-interpolation 协议来研究由于隐藏层中的 permutation 对称性而导致的损失景观中相同区域副本之间的联系;(3)使用分层聚类来揭示 DNN 训练解之间的层次结构,这让人联想到所谓的复制对称性破坏(RSB)现象(即巴黎解)。(4) 最后,我们研究了 DNN 损失景观的崎岖程度与 DNN 普适性之间的关系,显示了扁平化最小值的改进。
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引用次数: 0
Coarse geometric approach to topological phases: Invariants from real-space representations 拓扑相位的粗几何方法:来自实空间表示的不变式
Pub Date : 2024-07-23 DOI: arxiv-2407.16494
Christoph S. Setescak, Caio Lewenkopf, Matthias Ludewig
We show that topological phases include disordered materials if theunderlying invariant is interpreted as originating from coarse geometry. Thiscoarse geometric framework, grounded in physical principles, offers a naturalsetting for the bulk-boundary correspondence, reproduces physical knowledge,and leads to an efficient and tractable numerical approach for calculatinginvariants. As a showcase, we give a detailed discussion of the framework forthree-dimensional systems with time-reversal symmetry. We numerically reproducethe known disorder-free phase diagram of a tunable, effective tight-bindingmodel and analyze the evolution of the topological phase under disorder.
我们证明,如果将基本不变式解释为源于粗几何,拓扑相包括无序材料。这种粗几何框架以物理原理为基础,为体界对应关系提供了一个自然设置,再现了物理知识,并为计算不变式提供了一种高效、可操作的数值方法。作为展示,我们详细讨论了具有时间反转对称性的三维系统的框架。我们用数值方法再现了一个可调有效紧密结合模型的已知无序相图,并分析了无序状态下拓扑相的演化。
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引用次数: 0
Some new results for the GHWS model GHWS 模型的一些新成果
Pub Date : 2024-07-19 DOI: arxiv-2407.14318
Leonardo Reyes
Here we outline some new results for the GHWS model which points to adiscretization of parameter space into well differentiated collective dynamicstates. We argue this can lead to basic processes in parameter space, startingwith minimum modelling ingredients: a complex network with a disorder parameterand an excitable dynamics (cellular automata) on it.
在此,我们概述了 GHWS 模型的一些新成果,这些成果指出了将参数空间离散化为分化良好的集体动力学状态的可能性。我们认为,这可以导致参数空间中的基本过程,从最小的建模成分开始:一个具有无序参数的复杂网络和其上的可激发动力学(细胞自动机)。
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引用次数: 0
Phase induced localization transition 相位诱导定位转换
Pub Date : 2024-07-14 DOI: arxiv-2407.10043
Tong Liu, Xingbo Wei, Youguo Wang
Localization phenomenon is an important research field in condensed matterphysics. However, due to the complexity and subtlety of disordered syestems,new localization phenomena always emerge unexpectedly. For example, it isgenerally believed that the phase of the hopping term does not affect thelocalization properties of the system, so the calculation of the phase is oftenignored in the study of localization. Here, we introduce a quasiperiodic modeland demonstrate that the phase change of the hopping term can significantlyalter the localization properties of the system through detailed numericalsimulations such as the inverse participation ratio and multifractal analysis.This phase-induced localization transition provides valuable information forthe study of localization physics.
局域化现象是凝聚态物理的一个重要研究领域。然而,由于无序系统的复杂性和微妙性,新的局域化现象总是出人意料地出现。例如,人们普遍认为跳变项的相位不会影响系统的局域特性,因此在局域化研究中往往忽略了相位的计算。在这里,我们引入了一个准周期模型,并通过详细的数值模拟,如反参与比和多分形分析,证明了跳变项的相位变化会显著改变系统的局域化特性。
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引用次数: 0
Statistical Localization of Electromagnetic Signals in Disordered Time-Varying Cavity 无序时变腔体内电磁信号的统计定位
Pub Date : 2024-07-12 DOI: arxiv-2407.21023
Bo Zhou, Xingsong Feng, Xianmin Guo, Fei Gao, Hongsheng Chen, Zuojia Wang
In this letter, we investigate the statistical properties of electromagneticsignals after different times of duration within one-dimensionallocal-disordered time-varying cavities, where both spatial and temporaldisorders are added. Our findings reveal that, in the vast majority of cases,adequate temporal disorder in local space can make the electromagnetic fieldstatistically localized, obeying a normal distribution at a specific point intime of arbitrary location within the cavity. We employ the concept ofdisordered space-time crystals and leverage Lindeberg's and Lyapunov's theoremsto theoretically prove the normal distribution of the field values.Furthermore, we find that with the increase of energy provided by timevariation, the probability of extreme fields will significantly increase andthe field intensity eventually is de-normalized, that is, deviating from thenormal distribution. This study not only sheds light on the statisticalproperties of transient signals in local-disordered time-varying systems butalso paves the way for further exploration in wave dynamics of analogoussystems.
在这封信中,我们研究了电磁学信号在一维局部无序时变空腔内持续不同时间后的统计特性。我们的研究结果表明,在绝大多数情况下,局部空间中充分的时间无序可以使电磁场统计局部化,在空腔内任意位置的特定时间点上服从正态分布。此外,我们还发现,随着时间变异提供的能量的增加,出现极端场的概率将显著增加,场强最终会去正态化,即偏离正态分布。这项研究不仅揭示了局部无序时变系统中瞬态信号的统计特性,而且为进一步探索类似系统的波动力学铺平了道路。
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引用次数: 0
Encoding arbitrary Ising Hamiltonians on Spatial Photonic Ising Machines 在空间光子伊辛机上编码任意伊辛哈密顿子
Pub Date : 2024-07-12 DOI: arxiv-2407.09161
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 reducedto the problem of finding the ground state of an Ising model. Spatial PhotonicIsing Machines have proven to be advantageous for simulating fully connectedlarge-scale spin systems. However, fine control of a general interaction matrix$J$ has so far only been accomplished through eigenvalue decomposition methodsthat either limit the scalability or increase the execution time of theoptimization process. We introduce and experimentally validate a SPIM instancethat enables direct control over the full interaction matrix, enabling theencoding of Ising Hamiltonians with arbitrary couplings and connectivity. Wedemonstrate the conformity of the experimentally measured Ising energy with thetheoretically expected values and then proceed to solve both the unweighted andweighted graph partitioning problems, showcasing a systematic convergence to anoptimal solution via simulated annealing. Our approach greatly expands theapplicability of SPIMs for real-world applications without sacrificing any ofthe inherent advantages of the system, and paves the way to encoding the fullrange of NP problems that are known to be equivalent to Ising models, on SPIMdevices.
光子伊辛机是一种新兴的计算范式,旨在解决可简化为寻找伊辛模型基态的组合优化问题。事实证明,空间光子伊兴机在模拟完全连接的大规模自旋系统方面具有优势。然而,迄今为止,对一般相互作用矩阵$J$的精细控制只能通过特征值分解方法来实现,这种方法要么限制了可扩展性,要么增加了优化过程的执行时间。我们引入并通过实验验证了一种 SPIM 实例,它可以直接控制整个相互作用矩阵,从而可以对具有任意耦合和连通性的伊辛哈密顿进行编码。我们证明了实验测量的伊辛能量与理论预期值的一致性,然后继续解决非加权和加权图分割问题,通过模拟退火展示了向最优解的系统性收敛。我们的方法在不牺牲系统固有优势的前提下,极大地扩展了 SPIM 在实际应用中的适用性,并为在 SPIM 设备上编码已知等价于 Ising 模型的所有 NP 问题铺平了道路。
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引用次数: 0
A Very Effective and Simple Diffusion Reconstruction for the Diluted Ising Model 针对稀释伊辛模型的非常有效而简单的扩散重构
Pub Date : 2024-07-09 DOI: arxiv-2407.07266
Stefano Bae, Enzo Marinari, Federico Ricci-Tersenghi
Diffusion-based generative models are machine learning models that usediffusion processes to learn the probability distribution of high-dimensionaldata. In recent years, they have become extremely successful in generatingmultimedia content. However, it is still unknown if such models can be used togenerate high-quality datasets of physical models. In this work, we use aLandau-Ginzburg-like diffusion model to infer the distribution of a $2D$bond-diluted Ising model. Our approach is simple and effective, and we showthat the generated samples reproduce correctly the statistical and criticalproperties of the physical model.
基于扩散的生成模型是一种使用扩散过程来学习高维数据概率分布的机器学习模型。近年来,它们在生成多媒体内容方面取得了巨大成功。然而,这种模型能否用于生成高质量的物理模型数据集,目前还不得而知。在这项工作中,我们使用类似兰道-金兹堡的扩散模型来推断一个 2D 美元债券稀释伊辛模型的分布。我们的方法简单而有效,并证明生成的样本正确再现了物理模型的统计和临界特性。
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引用次数: 0
About the AT line in Replica Symmetry Breaking assumption for spin glasses 关于自旋玻璃的复制对称性破缺假设中的 AT 线
Pub Date : 2024-07-09 DOI: arxiv-2407.06701
Linda Albanese
Replica Symmetry Breaking is a fascinating phenomenon of spin glasses modelwhich could have consequences also in other field of studies. Although thereare several studies regarding the stability between the Replica Symmetric andfirst step of Replica Symmetry Breaking approximations, we do not have resultsfor the following steps (apart from that one by Gardner for P-spin glasses in1985). This is link to the fact that the classic method, based from the work byDe 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 devisea new straightforward method inspired to the work by Toninelli in 2002 torecover the critical line in order to inspect the stability between the secondstep of Replica Symmetry Breaking and the first one. Moreover, we generalise toKth 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。
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引用次数: 0
期刊
arXiv - PHYS - Disordered Systems and Neural Networks
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