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Effects of setting temperatures in the parallel tempering Monte Carlo algorithm

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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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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Strongly fluctuating moments in the high-temperature magnetic superconductor RbEuFe4As4

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Physical Review B 2019年第18期99卷 180502(R)-180502(R)页

作者： K. Willa R. Willa J.-K. Bao A. E. Koshelev D. Y. Chung M. G. Kanatzidis W.-K. Kwok U. Welp Materials Science Division Argonne National Laboratory 9700 South Cass Avenue Lemont Illinois 60439 USA Department of Chemistry Northwestern University Evanston Illinois 60208 USA

The iron-based superconductor RbEuFe4As4 undergoes a magnetic phase transition deep in the superconducting state. We investigate the calorimetric response of RbEuFe4As4 single crystals of the magnetic and the superconducting phase and its anisotropy to in-plane and out-of-plane magnetic fields. Whereas the unusual cusplike anomaly associated with the magnetic transition is suppressed to lower temperatures for fields along the crystallographic c axis, it rapidly transforms to a broad shoulder shifting to higher temperatures for in-plane fields. We identify the cusp in the specific-heat data as a Berezinskii-Kosterlitz-Thouless transition with fine features caused by the three-dimensional effects. The high-temperature shoulder in high magnetic fields marks a crossover from a paramagnetically disordered to an ordered state. This observation is further supported by Monte Carlo simulations of an easy-plane two-dimensional Heisenberg model and a fourth-order high-temperature expansion, both of which agree qualitatively and quantitatively with the experimental findings.

关键词： BKT transition Exchange interaction Magnetic anisotropy Magnetic phase transitions 2-dimensional systems Iron-based superconductors Pnictides Calorimetry Heisenberg model metropolis algorithm Specific heat measurements Spin lattice models

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Acceptance rate is a thermodynamic function in local Monte Carlo algorithms

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Physical Review E 2019年第6期100卷 063303-063303页

作者： Evgeni Burovski Wolfhard Janke Maria Guskova Lev Shchur National Research University Higher School of Economics 101000 Moscow Russia Institut für Theoretische Physik Universität Leipzig IPF 231101 04081 Leipzig Germany Landau Institute for Theoretical Physics 142432 Chernogolovka Russia

We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the three- and four-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.

关键词： Classical statistical mechanics Classical spin models Heatbath algorithm metropolis algorithm Monte Carlo methods

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Fusion Channels of Non-Abelian Anyons from Angular-Momentum and Density-Profile Measurements

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Physical Review Letters 2019年第26期123卷 266801-266801页

作者： E. Macaluso T. Comparin L. Mazza I. Carusotto INO-CNR BEC Center and Dipartimento di Fisica Università di Trento 38123 Trento Italy LPTMS CNRS Université Paris-Sud Université Paris-Saclay 91405 Orsay France

We present a method to characterize non-Abelian anyons that is based only on static measurements and that does not rely on any form of interference. For geometries where the anyonic statistics can be revealed by rigid rotations of the anyons, we link this property to the angular momentum of the initial state. We test our method on the paradigmatic example of the Moore-Read state that is known to support excitations with non-Abelian statistics of Ising type. As an example, we reveal the presence of different fusion channels for two such excitations, a defining feature of non-Abelian anyons. This is obtained by measuring density-profile properties, like the mean square radius of the system or the depletion generated by the anyons. Our study paves the way to novel methods for characterizing non-Abelian anyons, both in the experimental and theoretical domains.

关键词： Anyons Fractional quantum Hall effect Geometric & topological phases Strongly correlated systems Ultracold gases metropolis algorithm

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Monte Carlo methods

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GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS 2018年第1期9卷 117-143页

作者： Koch, Karl-Rudolf Univ Bonn Inst Geodesy & Geoinformat Theoret Geodesy Grp Nussallee 17 D-53115 Bonn Germany

Monte Carlo methods deal with generating random variates from probability density functions in order to estimate unknown parameters or general functions of unknown parameters and to compute their expected values, variances and covariances. One generally works with the multivariate normal distribution due to the central limit theorem. However, if random variables with the normal distribution and random variables with a different distribution are combined, the normal distribution is not valid anymore. The Monte Carlo method is then needed to get the expected values, variances and covariances for the random variables with distributions different from the normal distribution. The error propagation by Monte Carlo methods is discussed and methods for generating random variates from the multivariate normal distribution and from the multivariate uniform distribution. The Monte Carlo integration is presented leading to the sampling-importance-resampling algorithm. Markov chain Monte Carlo methods provide by the metropolis algorithm and the Gibbs sampler additional ways of generating random variates. A special topic is the Gibbs sampler for computing and propagating large covariance matrices. This task arises, for instance, when the geopotential is determined from satellite observations. The example of the minimal detectable outlier shows, how the Monte Carlo method is used to determine the power of a hypothesis test.

关键词： Bayesian statistics SIR algorithm metropolis algorithm Gibbs sampler Markov chain Monte Carlo methods

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Large deviations of the length of the longest increasing subsequence of random permutations and random walks

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Physical Review E 2019年第4期99卷 042104-042104页

作者： Jörn Börjes Hendrik Schawe Alexander K. Hartmann Institut für Physik Universität Oldenburg 26111 Oldenburg Germany

We study numerically the length distribution of the longest increasing subsequence (LIS) for random permutations and one-dimensional random walks. Using sophisticated large-deviation algorithms, we are able to obtain very large parts of the distribution, especially also covering probabilities smaller than 10−1000. This enables us to verify for the length of the LIS of random permutations the analytically known asymptotics of the rate function and even the whole Tracy-Widom distribution. We observe a rather fast convergence in the larger than typical part to this limiting distribution. For the length L of LIS of random walks no analytical results are known to us. We test a proposed scaling law and observe convergence of the tails into a collapse for increasing system size. Further, we obtain estimates for the leading-order behavior of the rate functions in both tails.

关键词： Random walks Large deviation & rare event statistics metropolis algorithm

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Evidence of Kosterlitz-Thouless phase transitions in the Ising model with dipolar interactions

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Physical Review E 2019年第2期100卷 022143-022143页

作者： M. A. Bab G. P. Saracco Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas (INIFTA) UNLP CCT La Plata-CONICET c.c. 16 Suc. 4 (1900)La Plata Argentina

The ferromagnetic bidimensional Ising model with dipolar interactions has been proposed to model ultrathin films with strong out-of-plane anisotropy. The phase diagram presents a rich phenomenology that includes low-temperature phases characterized by stripes of width n (hn) and a high-temperature phase with domains of stripes with mutually perpendicular orientations, named tetragonal liquid (TL). The latter phase can be reached by two possible ways. One of them is the direct transition hn to TL, and the other one is through an intermediate phase with orientational order but short-range positional disorder, named nematic phase (NM). The regions of the phase diagram where these transitions occur, as well as their character, remain an open question and are the object of the present work. In order to clarify this topic, intensive Monte Carlo simulations were performed by employing short-time dynamics as the main tool for studying the phase transition behavior. The dynamic evolution of the orientational order parameter and its moments are measured for selected values of the ratio between the ferromagnetic exchange and dipolar constants, called δ. The obtained results indicate that the intermediate NM phase is present for δ≥2 in narrow ranges of temperatures. Also, the results suggest that both transitions, i.e., hn-NM and NM-TL, have a Kosterlitz-Thouless character. This type of topological transition is observed in continuous bidimensional models and have been proposed for discrete ones, as in the case of the present work.

关键词： Critical phenomena Magnetic phase transitions Nematic phase transition Phase diagrams Phase transitions Lattice models in statistical physics Thin films metropolis algorithm Monte Carlo methods

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Exotic Magnetic Field-Induced Spin-Superstructures in a Mixed Honeycomb-Triangular Lattice System

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Physical Review X 2019年第1期9卷 011038-011038页

作者： V. Ovidiu Garlea Liurukara D. Sanjeewa Michael A. McGuire Cristian D. Batista Anjana M. Samarakoon David Graf Barry Winn Feng Ye Christina Hoffmann Joseph W. Kolis Neutron Scattering Division Oak Ridge National Laboratory Oak Ridge Tennessee 37831 USA Department of Chemistry and Center for Optical Materials Science and Engineering Technologies (COMSET) Clemson University Clemson South Carolina 29634-0973 USA Materials Science and Technology Division Oak Ridge National Laboratory Oak Ridge Tennessee 37831 USA Shull-Wollan Center Oak Ridge National Laboratory Oak Ridge Tennessee 37831 USA Department of Physics and Astronomy University of Tennessee Knoxville Tennessee 37996 USA National High Magnetic Field Laboratory Florida State University Tallahassee Florida 32310 USA

The temperature–magnetic field phase diagram of the mixed honeycomb-triangular lattice system K2Mn3(VO4)2CO3 is investigated by means of magnetization, heat-capacity, and neutron-scattering measurements. The results indicate that triangular and honeycomb magnetic layers undergo sequential magnetic orderings and act as nearly independent magnetic sublattices. The honeycomb sublattice orders at about 85 K in a Neél-type antiferromagnetic structure, while the triangular sublattice displays two consecutive ordered states at much lower temperatures, 3 and 2.2 K. The ground state of the triangular sublattice consists of a planar “Y” magnetic structure that emerges from an intermediate collinear “up-up-down” state. Applied magnetic fields parallel or perpendicular to the c axis induce exotic ordered phases characterized by various spin-stacking sequences of triangular layers that yield bilayer, three-layer, or four-layer magnetic superstructures. The observed superstructures cannot be explained in the framework of quasiclassical theory based only on nearest-neighbor interlayer coupling and point towards the presence of effective second-nearest-neighbor interactions mediated by fluctuations of the magnetic moments in the honeycomb sublattice.

关键词： Antiferromagnetism Exchange interaction Frustrated magnetism Spin state transition 2-dimensional systems Antiferromagnets Kagome lattice Crystal growth Holstein-Primakoff method Inelastic neutron scattering Magnetization measurements metropolis algorithm Neutron diffraction Specific heat measurements Susceptibility measurements

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Model of magnetic friction obeying the Dieterich-Ruina law in the steady state

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Physical Review E 2019年第5期100卷 052130-052130页

作者： Hisato Komatsu Research Center for Advanced Measurement and Characterization National Institute for Materials Science Tsukuba Ibaraki 305-0047 Japan

We propose a model of magnetic friction and investigate the relation between the frictional force and the relative velocity of surfaces in the steady state. The model comprises two square lattices adjacent to each other, the upper of which is subjected to an external force, and the magnetic interaction acts as a kind of potential barrier that prevents the upper lattice from moving. We consider two surface types for the upper lattice: smooth and rough. The behavior of this model is classified into two domains, which we refer to as domains I and II. In domain II, the external force is dominant compared with other forces, whereas in domain I, the velocity of the lattice is suppressed by the magnetic interaction and obeys the Dieterich-Ruina law. This characteristic property can be observed regardless of whether the surface is smooth or rough.

关键词： Friction Nonequilibrium statistical mechanics Classical spin models Langevin algorithm metropolis algorithm

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