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Non-reciprocal spin-glass transition and aging 非互惠自旋玻璃转变和老化
Pub Date : 2024-08-30 DOI: arxiv-2408.17360
Giulia Garcia Lorenzana, Ada Altieri, Giulio Biroli, Michel Fruchart, Vincenzo Vitelli
Disordered systems generically exhibit aging and a glass transition. Previousstudies have long suggested that non-reciprocity tends to destroy glassiness.Here, we show that this is not always the case using a bipartite sphericalSherrington-Kirpatrick model that describes the antagonistic coupling betweentwo identical complex agents modeled as macroscopic spin glasses. Our dynamicalmean field theory calculations reveal an exceptional-point mediated transitionfrom a static disorder phase to an oscillating amorphous phase as well asnon-reciprocal aging with slow dynamics and oscillations.
无序系统通常会出现老化和玻璃化转变。在这里,我们使用一个双方球形谢林顿-基尔帕特里克模型,描述了被模拟为宏观自旋玻璃的两种相同复杂介质之间的拮抗耦合,结果表明情况并非总是如此。我们的动力学均场理论计算揭示了由例外点介导的从静态无序相到振荡无定形相的转变,以及具有缓慢动力学和振荡的非互惠老化。
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引用次数: 0
Nature of the onset to temperature chaos 温度混沌开始的性质
Pub Date : 2024-08-29 DOI: arxiv-2408.16874
Jiaming He, Hongze Li, Raymond Lee Orbach
Temperature chaos (TC) in spin glasses has been claimed to exist no matterhow small the temperature change, $Delta T$. However, experimental studiesexhibit a finite value of $Delta T$ for the transition to TC. This paperexplores the onset of TC with much higher accuracy over a large temperaturerange. We find that TC is always present, though small for the smallest $DeltaT$ that we can reliably measure. However, it grows rapidly as $Delta T$increases, the region of rapid growth coinciding with the $Delta T$ predictedfrom renormalization group arguments and observed experimentally. We are ableto transcend the full range for the onset of TC, from fully reversible to fullychaotic.
自旋玻璃中的温度混沌(TC)被认为无论温度变化多小都会存在。然而,实验研究表明,过渡到 TC 的 $Delta T$ 值是有限的。本论文在较大的温度范围内以更高的精度探讨了TC的发生。我们发现,TC 始终存在,尽管在我们能可靠测量的最小 $DeltaT$ 时很小。然而,它随着 $Delta T$ 的增加而迅速增长,快速增长的区域与重正化组论证预测并在实验中观察到的 $Delta T$ 相吻合。我们能够超越从完全可逆到完全混乱的TC起始的全部范围。
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引用次数: 0
Autoregressive model path dependence near Ising criticality 伊辛临界附近的自回归模型路径依赖性
Pub Date : 2024-08-28 DOI: arxiv-2408.15715
Yi Hong Teoh, Roger G. Melko
Autoregressive models are a class of generative model that probabilisticallypredict the next output of a sequence based on previous inputs. Theautoregressive sequence is by definition one-dimensional (1D), which is naturalfor language tasks and hence an important component of modern architectureslike recurrent neural networks (RNNs) and transformers. However, when languagemodels are used to predict outputs on physical systems that are notintrinsically 1D, the question arises of which choice of autoregressivesequence -- if any -- is optimal. In this paper, we study the reconstruction ofcritical correlations in the two-dimensional (2D) Ising model, using RNNs andtransformers trained on binary spin data obtained near the thermal phasetransition. We compare the training performance for a number of different 1Dautoregressive sequences imposed on finite-size 2D lattices. We find that pathswith long 1D segments are more efficient at training the autoregressive modelscompared to space-filling curves that better preserve the 2D locality. Ourresults illustrate the potential importance in choosing the optimalautoregressive sequence ordering when training modern language models for tasksin physics.
自回归模型是一类生成模型,它能根据先前的输入从概率上预测序列的下一个输出。自回归序列顾名思义是一维(1D)的,这对于语言任务来说很自然,因此也是循环神经网络(RNN)和变换器等现代架构的重要组成部分。然而,当语言模型被用于预测非一维物理系统的输出时,就出现了自回归方程的最佳选择问题。在本文中,我们使用在热相位转换附近获得的二元自旋数据上训练的 RNN 和变换器,研究了二维 (2D) 伊辛模型中临界相关性的重建。我们比较了施加在有限尺寸二维网格上的一系列不同一维自回归序列的训练性能。我们发现,在训练自回归模型时,具有长一维段的路径比空间填充曲线更有效,后者能更好地保持二维局部性。我们的研究结果说明,在为物理学任务训练现代语言模型时,选择最佳自回归序列排序具有潜在的重要性。
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引用次数: 0
Generalizations of Parisi's replica symmetry breaking and overlaps in random energy models 随机能量模型中帕里西复制对称性破缺和重叠的一般化
Pub Date : 2024-08-27 DOI: arxiv-2408.15125
Bernard Derrida, Peter Mottishaw
The random energy model (REM) is the simplest spin glass model which exhibitsreplica symmetry breaking. It is well known since the 80's that its overlapsare non-selfaveraging and that their statistics satisfy the predictions of thereplica theory. All these statistical properties can be understood byconsidering that the low energy levels are the points generated by a Poissonprocess with an exponential density. Here we first show how, by replacing theexponential density by a sum of two exponentials, the overlaps statistics aremodified. One way to reconcile these results with the replica theory is toallow the blocks in the Parisi matrix to fluctuate. Other examples where thesizes of these blocks should fluctuate include the finite size corrections ofthe REM, the case of discrete energies and the overlaps between twotemperatures. In all these cases, the blocks sizes not only fluctuate but needto take complex values if one wishes to reproduce the results of ourreplica-free calculations.
随机能量模型(REM)是最简单的自旋玻璃模型,表现出复制对称性破缺。自上世纪 80 年代以来,人们就清楚地知道它的重叠是非自平均的,而且其统计特性满足复制理论的预测。考虑到低能级是由具有指数密度的泊松过程产生的点,就可以理解所有这些统计特性。在这里,我们首先展示了用两个指数之和取代指数密度后,重叠统计是如何被修正的。将这些结果与复制理论相协调的一种方法是允许帕里西矩阵中的块发生波动。这些块的大小应该波动的其他例子包括 REM 的有限尺寸修正、离散能量的情况以及两个温度之间的重叠。在所有这些情况下,如果要重现我们的无复制品计算结果,这些块的大小不仅会波动,而且需要取复杂的值。
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引用次数: 0
Stochastic quantum models for the dynamics of power grids 电网动态的随机量子模型
Pub Date : 2024-08-27 DOI: arxiv-2408.14921
Pierrick Guichard, Nicolas Retière, Didier Mayou
While electric power grids play a key role in the decarbonization of society,it remains unclear how recent trends, such as the strong integration ofrenewable energies, can affect their stability. Power oscillation modes, whichare key to the stability of the grid, are traditionally studied numericallywith the conventional view-point of two regimes of extended (inter-area) orlocalized (intra-area) modes. In this article we introduce an analogy based onstochastic quantum models and demonstrate its applicability to power systems.We show from simple models that at low frequency the mean free path induced bydisorder is inversely cubic in the frequency. This stems from theCourant-Fisher-Weyl theorem, which predicts a strong protection of the lowestfrequency modes from disorder. As a consequence a power oscillation, induced bysome local disruption of the grid, can propagate in a ballistic, diffusive orlocalised regime. In contrast with the conventional view-point, the existenceof these three regimes is confirmed in a realistic model of the European powergrid.
尽管电网在社会去碳化过程中发挥着关键作用,但目前仍不清楚可再生能源的大力整合等最新趋势会如何影响电网的稳定性。电力振荡模式是电网稳定性的关键所在,传统的数值研究通常从扩展模式(区域间)或局部模式(区域内)两种状态的传统视角出发。在本文中,我们介绍了一种基于随机量子模型的类比方法,并展示了其在电力系统中的适用性。我们通过简单的模型证明,在低频情况下,由无序引起的平均自由路径与频率成反立方关系。这源于库朗-费舍尔-韦尔定理(Courant-Fisher-Weyl theorem),该定理预言最低频率的模式会受到无序的强烈保护。因此,由网格局部破坏引起的功率振荡可以在弹道、扩散或局部机制中传播。与传统观点不同的是,欧洲电网的现实模型证实了这三种机制的存在。
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引用次数: 0
Guerra interpolation for place cells 地方单元的格拉插值
Pub Date : 2024-08-25 DOI: arxiv-2408.13856
Martino Salomone Centonze, Alessandro Treves, Elena Agliari, Adriano Barra
Pyramidal cells that emit spikes when the animal is at specific locations ofthe environment are known as "place cells": these neurons are thought toprovide an internal representation of space via "cognitive maps". Here, weconsider the Battaglia-Treves neural network model for cognitive map storageand reconstruction, instantiated with McCulloch & Pitts binary neurons. Toquantify the information processing capabilities of these networks, we exploitspin-glass techniques based on Guerra's interpolation: in the low-storageregime (i.e., when the number of stored maps scales sub-linearly with thenetwork size and the order parameters self-average around their means) weobtain an exact phase diagram in the noise vs inhibition strength plane (inagreement with previous findings) by adapting the Hamilton-Jacobi PDE-approach.Conversely, in the high-storage regime, we find that -- for mild inhibition andnot too high noise -- memorization and retrieval of an extensive number ofspatial maps is indeed possible, since the maximal storage capacity is shown tobe strictly positive. These results, holding under the replica-symmetryassumption, are obtained by adapting the standard interpolation based onstochastic stability and are further corroborated by Monte Carlo simulations(and replica-trick outcomes for the sake of completeness). Finally, by relyingupon an interpretation in terms of hidden units, in the last part of the work,we adapt the Battaglia-Treves model to cope with more general frameworks, suchas bats flying in long tunnels.
当动物处于环境的特定位置时会发出尖峰的锥体细胞被称为 "位置细胞":这些神经元被认为是通过 "认知地图 "提供空间的内部表征。在此,我们将考虑使用 McCulloch 和 Pitts 二元神经元实例化的认知地图存储和重建的巴塔利亚-特雷弗斯神经网络模型。为了量化这些网络的信息处理能力,我们利用了基于格拉插值法的旋镜技术:在低存储时间(即相反,在高存储条件下,我们发现--在轻度抑制和噪声不太高的情况下--记忆和检索大量空间地图确实是可能的,因为最大存储容量被证明是严格的正值。这些结果在复制对称假设下成立,是通过调整基于随机稳定性的标准内插法得到的,并通过蒙特卡罗模拟(为完整起见,还包括复制技巧结果)得到进一步证实。最后,通过对隐藏单元的解释,我们在工作的最后一部分调整了巴塔利亚-特雷弗斯模型,以应对更一般的框架,如在长隧道中飞行的蝙蝠。
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引用次数: 0
A cost-effective strategy of enhancing machine learning potentials by transfer learning from a multicomponent dataset on ænet-PyTorch 通过在 ænet-PyTorch 上对多组件数据集进行迁移学习来增强机器学习潜力的经济高效战略
Pub Date : 2024-08-23 DOI: arxiv-2408.12939
An Niza El Aisnadaa, Kajjana Boonpalit Robin van der Kruit, Koen M. Draijer, Jon Lopez-Zorrilla, Masahiro Miyauchi, Akira Yamaguchi, Nongnuch Artrith
Machine learning potentials (MLPs) offer efficient and accurate materialsimulations, but constructing the reference ab initio database remains asignificant challenge, particularly for catalyst-adsorbate systems. Training anMLP with a small dataset can lead to overfitting, thus limiting its practicalapplications. This study explores the feasibility of developing computationallycost-effective and accurate MLPs for catalyst-adsorbate systems with a limitednumber of ab initio references by leveraging a transfer learning strategy fromsubsets of a comprehensive public database. Using the Open Catalyst Project2020 (OC20) -- a dataset closely related to our system of interest -- wepre-trained MLP models on OC20 subsets using the {ae}net-PyTorch framework. Wecompared several strategies for database subset selection. Our findingsindicate that MLPs constructed via transfer learning exhibit bettergeneralizability than those constructed from scratch, as demonstrated by theconsistency in the dynamics simulations. Remarkably, transfer learning enhancesthe stability and accuracy of MLPs for the CuAu/H2O system with approximately600 reference data points. This approach achieved excellent extrapolationperformance in molecular dynamics (MD) simulations for the larger CuAu/6H2Osystem, sustaining up to 250 ps, whereas MLPs without transfer learning lastedless than 50 ps. We also examine the potential limitations of this strategy.This work proposes an alternative, cost-effective approach for constructingMLPs for the challenging simulation of catalytic systems. Finally, weanticipate that this methodology will pave the way for broader applications inmaterial science and catalysis research, facilitating more efficient andaccurate simulations across various systems.
机器学习势能(MLP)可提供高效、准确的材料模拟,但构建参考的 ab initio 数据库仍是一项重大挑战,尤其是对于催化剂-吸附剂系统而言。用小数据集训练 MLP 可能会导致过度拟合,从而限制其实际应用。本研究通过利用综合公共数据库子集的迁移学习策略,探索了为催化剂吸附剂系统开发计算成本低、准确性高的 MLP 的可行性。利用开放催化剂项目2020(OC20)--一个与我们感兴趣的系统密切相关的数据集--我们使用{ae}net-PyTorch框架在OC20子集上预先训练了MLP模型。我们比较了几种数据库子集选择策略。我们的研究结果表明,通过迁移学习构建的 MLP 比从头开始构建的 MLP 具有更好的泛化能力,动态模拟的一致性也证明了这一点。值得注意的是,迁移学习增强了具有约 600 个参考数据点的 CuAu/H2O 系统 MLP 的稳定性和准确性。这种方法在更大的 CuAu/6H2O 系统的分子动力学(MD)模拟中实现了出色的外推性能,可持续长达 250 ps,而没有迁移学习的 MLP 持续时间不到 50 ps。我们还研究了这一策略的潜在局限性。这项工作提出了一种替代性的、具有成本效益的方法,用于构建具有挑战性的催化系统模拟的 MLPs。最后,我们预计这种方法将为材料科学和催化研究的更广泛应用铺平道路,促进对各种系统进行更高效、更精确的模拟。
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引用次数: 0
Dynamics of Meta-learning Representation in the Teacher-student Scenario 师生情景中元学习表征的动态变化
Pub Date : 2024-08-22 DOI: arxiv-2408.12545
Hui Wang, Cho Tung Yip, Bo Li
Gradient-based meta-learning algorithms have gained popularity for theirability to train models on new tasks using limited data. Empirical observationsindicate that such algorithms are able to learn a shared representation acrosstasks, which is regarded as a key factor in their success. However, thein-depth theoretical understanding of the learning dynamics and the origin ofthe shared representation remains underdeveloped. In this work, we investigatethe meta-learning dynamics of the non-linear two-layer neural networks trainedon streaming tasks in the teach-student scenario. Through the lens ofstatistical physics analysis, we characterize the macroscopic behavior of themeta-training processes, the formation of the shared representation, and thegeneralization ability of the model on new tasks. The analysis also points tothe importance of the choice of certain hyper-parameters of the learningalgorithms.
基于梯度的元学习算法能够利用有限的数据在新任务上训练模型,因此广受欢迎。经验观察表明,这种算法能够在不同任务间学习共享表征,这被认为是其成功的关键因素。然而,对学习动态和共享表征起源的深入理论理解仍然不够。在这项工作中,我们研究了非线性双层神经网络的元学习动态,这些神经网络是在师生情景下的流式任务中训练的。通过统计物理学分析的视角,我们描述了元训练过程的宏观行为、共享表征的形成以及模型对新任务的泛化能力。分析还指出了学习算法中某些超参数选择的重要性。
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引用次数: 0
Quantum transport under oscillatory drive with disordered amplitude 振幅无序的振荡驱动下的量子输运
Pub Date : 2024-08-22 DOI: arxiv-2408.12653
Vatsana Tiwari, Sushanta Dattagupta, Devendra Singh Bhakuni, Auditya Sharma
We investigate the dynamics of non-interacting particles in a one-dimensionaltight-binding chain in the presence of an electric field with random amplitudedrawn from a Gaussian distribution, and explicitly focus on the nature ofquantum transport. We derive an exact expression for the probability propagatorand the mean-squared displacement in the clean limit and generalize it for thedisordered case using the Liouville operator method. Our analysis reveals thatin the presence a random static field, the system follows diffusive transport;however, an increase in the field strength causes a suppression in thetransport and thus results in disorder-induced localization. We further extendthe analysis for a time-dependent disordered electric field and show that thedynamics of mean-squared-displacement deviates from the parabolic path as thefield strength increases, unlike the clean limit where ballistic transportoccurs.
我们研究了存在高斯分布随机振幅电场的一维光结合链中非相互作用粒子的动力学,并明确关注量子输运的性质。我们推导出了清洁极限下概率传播者和均方位移的精确表达式,并利用柳维尔算子法对无序情况进行了概括。我们的分析表明,在存在随机静态场的情况下,系统遵循扩散输运;然而,场强的增加会导致输运抑制,从而导致无序诱导的局域化。我们进一步扩展了对随时间变化的无序电场的分析,结果表明,随着场强的增加,平均平方位移的动力学轨迹偏离了抛物线轨迹,这与发生弹道输运的清洁极限不同。
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引用次数: 0
Elastic electron scattering and localization in a chain with isotopic disorder 同位素无序链中的弹性电子散射和定位
Pub Date : 2024-08-20 DOI: arxiv-2408.10909
K. S. Denisov, E. Ya. Sherman
We study elastic electron scattering and localization by ubiquitous isotopicdisorder in one-dimensional systems appearing due to interaction with phononmodes localized at isotope impurities. By using a tight-binding model withintersite hopping matrix element dependent on the interatomic distance, we findmass-dependent backscattering probability by single and pairs of isotopicimpurities. For the pairs, in addition to the mass, the distance between theisotopes plays the critical role. Single impurities effectively attractelectrons and can produce localized weakly bound electron states. In thepresence of disorder, the electron free path at positive energies becomesfinite and the corresponding Anderson localization at the spatial scale greatlyexceeding the distance between the impurities becomes possible.
我们研究了一维系统中无处不在的同位素失序引起的弹性电子散射和局域化,这种散射和局域化是由于与同位素杂质处局域化的声子模式相互作用而产生的。通过使用与原子间距离有关的短距跳变矩阵元素的紧密结合模型,我们发现了单个和成对同位素杂质的反向散射概率与质量有关。对于成对的杂质,除了质量之外,同位素之间的距离也起着关键作用。单个杂质能有效地吸引电子,并产生局部的弱结合电子态。在存在无序的情况下,电子在正能量下的自由路径变得无限,相应的安德森定位在大大超过杂质间距离的空间尺度上成为可能。
{"title":"Elastic electron scattering and localization in a chain with isotopic disorder","authors":"K. S. Denisov, E. Ya. Sherman","doi":"arxiv-2408.10909","DOIUrl":"https://doi.org/arxiv-2408.10909","url":null,"abstract":"We study elastic electron scattering and localization by ubiquitous isotopic\u0000disorder in one-dimensional systems appearing due to interaction with phonon\u0000modes localized at isotope impurities. By using a tight-binding model with\u0000intersite hopping matrix element dependent on the interatomic distance, we find\u0000mass-dependent backscattering probability by single and pairs of isotopic\u0000impurities. For the pairs, in addition to the mass, the distance between the\u0000isotopes plays the critical role. Single impurities effectively attract\u0000electrons and can produce localized weakly bound electron states. In the\u0000presence of disorder, the electron free path at positive energies becomes\u0000finite and the corresponding Anderson localization at the spatial scale greatly\u0000exceeding the distance between the impurities becomes possible.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220867","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}
引用次数: 0
期刊
arXiv - PHYS - Disordered Systems and Neural Networks
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