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Fluctuation-based fracture mechanics of heterogeneous materials

Physical Review E 2022年第6期106卷 065003-065003页

作者： T. Mulla R. J.-M. Pellenq F.-J. Ulm Department of Civil and Environmental Engineering Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA MIT-CNRS-AMU Joint Laboratory Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Department of Physics Georgetown University Washington DC USA

We present results of a hybrid analytical-simulation investigation of the fracture resistance of heterogeneous materials. We show that bond-energy fluctuations sampled by Monte Carlo simulations in the semigrand canonical ensemble provide a means to rationalize the complexity of heterogeneous fracture processes, encompassing probability and percolation theories of fracture. For a number of random and textured model materials, we derive upper and lower bounds of fracture resistance and link bond fracture fluctuations to statistical descriptors of heterogeneity, such as two-point correlation functions, to identify the origin of toughening mechanisms. This includes a shift from short- to long-range interactions of bond fracture processes in random systems to the transition from critical to subcritical bond fracture percolation in textured materials and the activation of toughness reserves at compliant interfaces. Induced by elastic mismatch, they connect to a number of disparate experimental observations, including toughening of brittle solids by deformable polymers or organics in, e.g., gas shale, nacre; stress-induced transformational toughening in ceramics; and toughening of sparse elastic networks in hydrogels, to name a few.

关键词： Fluctuations & noise Fracture Percolation metropolis algorithm

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Monte Carlo study of the phase diagram of layered XY antiferromagnet

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2022年 605卷

作者： Acharyya, Muktish Vatansever, Erol Presidency Univ Dept Phys 86-1 Coll St Kolkata 700073 India Dokuz Eylul Univ Dept Phys TR-35160 Izmir Turkey

The three-dimensional XY model is investigated in the presence of a uniform magnetic field applied in the X-direction. The nearest neighbour intraplanar interaction is consid-ered ferromagnetic, and the interplanar nearest neighbour interaction is chosen to be antiferromagnetic. Starting from a high-temperature initial random spin configuration, the equilibrium phase of the system at any finite temperature was achieved by cooling the system using the Monte Carlo single spin-flip metropolis algorithm with a random updating rule. The components of total magnetization and the sublattice magnetizations were calculated. The variance of the antiferromagnetic order parameter and the sus-ceptibility have been calculated. In a specific range of relative strengths of interactions (antiferromagnetic/ferromagnetic) and the applied magnetic field, the system shows the equilibrium phase transitions at different temperatures. The phase diagrams (in the field-temperature plane) were obtained for different values of the relative interaction strengths. The ordered region bounded by the phase boundary was found to increase as the ratio of relative interaction strength increased. Furthermore, the maximum value of the susceptibility (chi aym) was found to increase with the system size (L). For chi aym & SIM;L gamma nu, the exponent gamma /nu has been estimated to be 2.10 & PLUSMN;0.11.(c) 2022 Elsevier B.V. All rights reserved.

关键词： XY model Monte Carlo simulation metropolis algorithm Layered antiferromagnet Scaling and critical exponent

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Dynamical generation of topological masses in Dirac fermions

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Physical Review B 2018年第8期97卷 081110(R)-081110(R)页

作者： Yuan-Yao He Xiao Yan Xu Kai Sun Fakher F. Assaad Zi Yang Meng Zhong-Yi Lu Department of Physics Renmin University of China Beijing 100872 China Beijing National Laboratory for Condensed Matter Physics Institute of Physics Chinese Academy of Sciences Beijing 100190 China School of Physical Sciences University of Chinese Academy of Sciences Beijing 100190 China Department of Physics University of Michigan Ann Arbor Michigan 48109 USA Institut für Theoretische Physik und Astrophysik Universität Würzburg 97074 Würzburg Germany

We report the discovery of a topological Mott insulator in strongly correlated Dirac semimetals. Such an interaction-driven topological state has been theoretically proposed and is observed here with unbiased large-scale numerical simulations. In our model, interactions between electrons are mediated by Ising spins in a transverse field. The results indicate that the topological mass term is dynamically generated and the resulting quantum phase transition belongs to the (two-plus-one-dimensional) N=8 chiral Ising universality class. These conclusions stem from large-scale sign-free quantum Monte Carlo simulations.

关键词： Phase transitions Quantum phase transitions Topological insulators Topological phases of matter Data analysis Finite-size scaling Lattice models in condensed matter metropolis algorithm Monte Carlo methods Path-integral methods Quantum Monte Carlo

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Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets

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Physical Review B 2023年第18期107卷 184418-184418页

作者： Emily Z. Zhang Reja H. Wilke Yong Baek Kim Department of Physics University of Toronto Toronto Ontario Canada M5S 1A7 Department of Physics Arnold Sommerfeld Center for Theoretical Physics Ludwig-Maximilians-Universität München 80333 Munich Germany

There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in α−RuCl3 in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the nonquantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is that the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behavior at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite-temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behavior near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results for existing and future experiments.

关键词： Frustrated magnetism Quantum spin liquid Spin dynamics Spin liquid metropolis algorithm Simulated annealing

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Effects of setting temperatures in the parallel tempering Monte Carlo algorithm

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Physical Review E 2019年第4期100卷 043311-043311页

作者： Ignacio Rozada Maliheh Aramon Jonathan Machta Helmut G. Katzgraber 1QB Information Technologies (1QBit) Vancouver BC V6C 2B5 Canada Physics Department University of Massachusetts Amherst Massachusetts 01003 USA Santa Fe Institute Santa Fe New Mexico 87501 USA Microsoft Quantum Microsoft Redmond Washington 98052 USA Department of Physics and Astronomy Texas A&M University College Station Texas 77843-4242 USA

Parallel tempering Monte Carlo has proven to be an efficient method in optimization and sampling applications. Having an optimized temperature set enhances the efficiency of the algorithm through more-frequent replica visits to the temperature limits. The approaches for finding an optimal temperature set can be divided into two main categories. The methods of the first category distribute the replicas such that the swapping ratio between neighboring replicas is constant and independent of the temperature values. The second-category techniques including the feedback-optimized method, on the other hand, aim for a temperature distribution that has higher density at simulation bottlenecks, resulting in temperature-dependent replica-exchange probabilities. In this paper, we compare the performance of various temperature setting methods on both sparse and fully connected spin-glass problems as well as fully connected Wishart problems that have planted solutions. These include two classes of problems that have either continuous or discontinuous phase transitions in the order parameter. Our results demonstrate that there is no performance advantage for the methods that promote nonuniform swapping probabilities on spin-glass problems where the order parameter has a smooth transition between phases at the critical temperature. However, on Wishart problems that have a first-order phase transition at low temperatures, the feedback-optimized method exhibits a time-to-solution speedup of at least a factor of two over the other approaches.

关键词： Optimization problems Ising model metropolis algorithm Monte Carlo methods

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Effect of a uniform random external magnetic field with spatiotemporal variation on compensation in Ising spin-1/2 trilayered square ferrimagnets

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Physical Review E 2021年第6期104卷 064126-064126页

作者： Soham Chandra Department of Physics Presidency University Kolkata 700 073 India

Trilayered spin-1/2 Ising ferrimagnets are interesting thin systems for compensation phenomenon. In this work, a metropolis Monte Carlo study is performed on the magnetic and thermodynamic response of such a system on square Bravais lattice, driven by uniform random external magnetic field with spatiotemporal variations. In two distinct configurations, the surface layers are made up of A and the middle layer is made up of B atoms in an ABA-type stacking while in AAB-type stacking, the top layer and the middle layer is made up of A atoms while the bottom layer is made up of B atoms. The magnetic coupling between the like atoms (A-A and B-B) is ferromagnetic while between the unlike atoms (A-B), it is antiferromagnetic. For the time-dependent external uniform random field, the mean is always set to zero and the standard deviation is varied until spin-field energy is comparable to the dominant cooperative energy of the system. The findings show that the observed compensation and critical points shift and steady-state magnetic behaviors shift among N, L, P, and Q, etc., type of ferrimagnetic behaviors, depending on the strength of external uniform random field. The compensation phenomenon even vanishes after crossing a finite threshold of standard deviation of the magnetic field for particular choices of the other controlling parameters. Thus islands of ferrimagnetic phase without compensation appear within the phase area with compensation of field-free case, in the two-dimensional Hamiltonian parameter space. For both the configurations, the areas of such islands even grow with increasing standard deviation of the external field, σ, obeying a scaling relation of the form: f(σ,A(σ))=σ−bA(σ) with bABA=1.958±0.122 and bAAB=1.783±0.118.

关键词： Ferrimagnets Magnetic multilayers Nonequilibrium lattice models metropolis algorithm

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State Aggregations in Markov Chains and Block Models of Networks

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Physical Review Letters 2021年第7期127卷 078301-078301页

作者： Mauro Faccin Michael T. Schaub Jean-Charles Delvenne ICTEAM Université catholique de Louvain 1348 Louvain-la-Neuve Belgium Department of Engineering Science University of Oxford Oxford OX1 2JD United Kingdom Department of Computer Science RWTH Aachen University 52074 Aachen Germany CORE Université catholique de Louvain 1348 Louvain-la-Neuve Belgium

We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T=1 this recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, which enables us to explain certain features of the likelihood landscape of this generative network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a timescale T≫1 is essential. We demonstrate our results using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans.

关键词： Clustering Community structure Geophysical networks Block models metropolis algorithm

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Few-shot machine learning in the three-dimensional Ising model

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Physical Review B 2019年第9期99卷 094427-094427页

作者： Rui Zhang Bin Wei Dong Zhang Jia-Ji Zhu Kai Chang SKLSM Institute of Semiconductors Chinese Academy of Sciences 100083 Beijing China Center for Excellence in Topological Quantum Computation University of Chinese Academy of Sciences Beijing 100190 China COT Design Department HiSilicon Technologies Co. Ltd. 518129 Shenzhen China School of Science and Laboratory of Quantum Information Technology Chongqing University of Posts and Telecommunications 400061 Chongqing China

We investigate theoretically the phase transition in a three-dimensional cubic Ising model utilizing state-of-the-art machine learning algorithms. Supervised machine learning models show high accuracies (99%) in phase classification and very small relative errors (<10−4) of the energies in different spin configurations. Unsupervised machine learning models are introduced to study the spin configuration reconstructions and reductions, and the phases of reconstructed spin configurations can be accurately classified by a linear logistic algorithm. Based on the comparison between various machine learning models, we develop a few-shot strategy to predict phase transitions in larger lattices from a trained sample in smaller lattices. The few-shot machine learning strategy for a three-dimensional (3D) Ising model enables us to study the 3D Ising model efficiently and provides an integrated and highly accurate approach to other spin models.

关键词： Magnetic order Magnetic phase transitions Phase transitions by order Ising model metropolis algorithm Monte Carlo methods

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Permutation glass

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Physical Review E 2018年第1期97卷 012139-012139页

作者： Mobolaji Williams Department of Physics Harvard University Cambridge Massachusetts 02138 USA

The field of disordered systems in statistical physics provides many simple models in which the competing influences of thermal and nonthermal disorder lead to new phases and nontrivial thermal behavior of order parameters. In this paper, we add a model to the subject by considering a disordered system where the state space consists of various orderings of a list. As in spin glasses, the disorder of such “permutation glasses” arises from a parameter in the Hamiltonian being drawn from a distribution of possible values, thus allowing nominally “incorrect orderings” to have lower energies than “correct orderings” in the space of permutations. We analyze a Gaussian, uniform, and symmetric Bernoulli distribution of energy costs, and, by employing Jensen's inequality, derive a simple condition requiring the permutation glass to always transition to the correctly ordered state at a temperature lower than that of the nondisordered system, provided that this correctly ordered state is accessible. We in turn find that in order for the correctly ordered state to be accessible, the probability that an incorrectly ordered component is energetically favored must be less than the inverse of the number of components in the system. We show that all of these results are consistent with a replica symmetric ansatz of the system. We conclude by arguing that there is no distinct permutation glass phase for the simplest model considered here and by discussing how to extend the analysis to more complex Hamiltonians capable of novel phase behavior and replica symmetry breaking. Finally, we outline an apparent correspondence between the presented system and a discrete-energy-level fermion gas. In all, the investigation introduces a class of exactly soluble models into statistical mechanics and provides a fertile ground to investigate statistical models of disorder.

关键词： Mathematical physics Disordered systems metropolis algorithm Replica methods

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Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding

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Physical Review E 2021年第6期103卷 062415-062415页

作者： Marco Ancona Alessandro Bentivoglio Michele Caraglio Giuseppe Gonnella Alessandro Pelizzola SUPA School of Physics and Astronomy University of Edinburgh Peter Guthrie Tait Road Edinburgh EH9 3FD United Kingdom Institut für Theoretische Physik Universität Innsbruck Technikerstraße 21A A-6020 Innsbruck Austria Dipartimento di Fisica Università degli Studi di Bari and INFN Sezione di Bari 70126 Bari Italy Dipartimento Scienza Applicata e Tecnologia Politecnico di Torino Corso Duca degli Abruzzi 24 10129 Torino Italy INFN Sezione di Torino via Pietro Giuria 1 10125 Torino Italy

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA or protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly interacting thermal bath. Notably, this “kinetic” temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple four-state Markov model which describes the long-time behavior of the RNA molecule.

关键词： Nonequilibrium & irreversible thermodynamics Nonequilibrium statistical mechanics Temperature Biomolecules Nonequilibrium systems Linear response theory metropolis algorithm Monte Carlo methods

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