Bulletin of the American Physical Society
APS March Meeting 2018
Volume 63, Number 1
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session A38: Advances in Computational Statistical Mechanics and their Applications: Part 1Focus
|
Hide Abstracts |
Sponsoring Units: DCOMP DCMP GSNP Chair: Dilina Perera, Texas A&M Univ Room: LACC 501A |
Monday, March 5, 2018 8:00AM - 8:12AM |
A38.00001: Variational Approach to Monte Carlo Renormalization Group Yantao Wu, Roberto Car We present a Monte Carlo method[1] for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The 2D Ising model is used to illustrate the method. |
Monday, March 5, 2018 8:12AM - 8:24AM |
A38.00002: Abstract Withdrawn
|
Monday, March 5, 2018 8:24AM - 8:36AM |
A38.00003: Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model Jiahao Xu, Alan Ferrenberg, David Landau While no analytic solution for the 3d Ising model exists, various numerical methods such as series expansion, Monte Carlo and MCRG have provided precise information about the phase transition. [1] Applying Monte Carlo simulation that employs the Wolff cluster flipping algorithm with both 32-bit and 53-bit random number generators, and analyzing data with histogram reweighting techniques and quadruple precision arithmetic, we have investigated the critical behavior of the 3d Ising Model, with lattice sizes ranging from 163 to 10243. By analyzing data with cross-correlations [2] between various thermodynamic quantities obtained from the same data pool, e.g. logarithmic derivatives of magnetization and energy cumulant, [3] we have obtained the critical inverse temperature Kc = 0.221 654 626(5) and the critical exponent of the correlation length ν = 0.629 912(86), and we will compare our results with the latest theoretical predictions. |
Monday, March 5, 2018 8:36AM - 8:48AM |
A38.00004: Critical nonequilibrium cluster-flip relaxations in Ising models Yusuke Tomita, Yoshihiko Nonomura At critical points, power-law relaxations are ubiquitously observed. In Monte Carlo simulations using local-update, the understanding of the relations between dynamical and critical exponents enable us to study critical phenomena by observing their power-law relaxations. On the other hand, little is known about relaxations in cluster-flip updates. Recently Nonomura claimed that critical nonequilibrium relaxation of the 2-dimensional Ising model by cluster-flip update is described by the stretched-exponential type [1]. Furthermore our consecutive studies confirmed that the stretched-exponential relaxation is ubiquitous in cluster-flip Monte Carlo simulations [2,3]. To understand the origin of the relaxation, we analyse the 2-, 3-, 4-dimensional, and infinite-range Ising models. While the infinite-range Ising model shows the simple exponential relaxation, the stretched-exponential relaxations are observed in finite dimensional Ising models. |
Monday, March 5, 2018 8:48AM - 9:00AM |
A38.00005: Nontrivial phase diagram for an elastic interaction model of spin crossover materials with antiferromagnetic-like short-range interactions Masamichi Nishino, Seiji Miyashita, Per Rikvold We investigate the phase diagram of an elastic interaction model for spin crossover materials with antiferromagnetic (AF)-like short-range (SR) interactions [1]. In this model, the interplay between the SR interaction and the long-range (LR) interaction of elastic origin causes complex phase transitions. For relatively weak elastic interactions, the phase diagram is characterized by tricritical points, at which AF-like and ferromagnetic (F)-like spinodal lines and a critical line merge. On the other hand, for relatively strong elastic interactions, unusual "horn structures," which are surrounded by the F-like spinodal lines, disorder (D) spinodal lines, and the critical line, are realized at higher temperatures. Similar structures of the phase diagram are found in the Ising AF magnet with infinite-range F interactions [2], and we find universal features caused by the interplay between the competing SR and LR interactions. The LR interaction of elastic origin is irrelevant (inessential) for the critical line. In contrast, those spinodal lines result from the LR interaction of elastic origin. |
Monday, March 5, 2018 9:00AM - 9:12AM |
A38.00006: Exploiting quantum classical crossover to undertake high performance modeling of magnetic materials David Tennant, Anjana Samarakoon, Ying Wai Li, Markus Eisenbach, Cristian Batista Massively parallel implementations of magnetic simulations present huge opportunities in materials discovery and identification. By combining with machine learning, such simulations have the potential to dramatically increase our understanding of spin networks both in terms of novel phase identification as well as revealing new physics. A forefront set of challenges are frustrated magnets and spin liquids. By comparing quantum and classical simulations, it is conjectured that at modest temperatures thermal fluctuations strongly de-phase quantum states and classical simulations become accurate. Here, detailed comparisons are made to many spin networks and quantum-classical crossover is demonstrated experimentally. In addition, the use of such simulations to uncover underlying new physics is shown. The use of advanced simulations and machine learning to accelerate discovery of materials, data analysis, and theoretical understanding are discussed. |
Monday, March 5, 2018 9:12AM - 9:48AM |
A38.00007: Abstract Withdrawn Invited Speaker:
|
Monday, March 5, 2018 9:48AM - 10:00AM |
A38.00008: Monte Carlo methods for massively parallel architectures Martin Weigel Scientists working with computer simulations need to move away from intrinsically serial algorithms to find new approaches that can make good use of potentially millions of cores. Monte Carlo methods based on Markov chains are intrinsically serial and hence are hard to parallelize. For short-range interactions one can use domain decompositions for parallel updates. A complementary approach simulates several chains in parallel, either at different temperatures such as in replica-exchange Monte Carlo or at the same temperature by simply pooling the statistics from independent runs. I review such methods and, in particular, focus on two especially promising approaches: firstly, a parallel variant of the multicanonical simulation method that uses independent walkers to speed up the convergence and shows close to perfect scaling up to 105 threads. Secondly, a sequential Monte Carlo method known as population annealing, that simulates a large population of configurations at the same temperature and then uses resampling and successive cooling. This approach is particularly suitable for parallel computing, and I disucc an efficient GPU implementation. A number of improvements turn it into a fully adaptive algorithm for the simulation of systems with complex free-energy landscapes. |
Monday, March 5, 2018 10:00AM - 10:12AM |
A38.00009: Efficiently Estimating the Density of States of Frustrated Systems Lev Barash, Itay Hen, Jeffrey Marshall, Martin Weigel Frustrated spin systems are known to stymie entropic samplers -- algorithms designed to statistically estimate the density of states at different energy intervals of physical systems. Intricate or rugged energy landscapes often cause these to yield false convergences to erroneous density estimations. Here, we report on the performance of a population annealing based algorithm on Ising spin glasses demonstrating orders of magnitude scaling advantages over exiting state-of-the-art algorithms. To demonstrate the algorithm's advantages in a verifiable manner, we introduce a scheme that allows us to achieve an exact count of the degeneracies of the ground- and first-excited states of the tested instances. We discuss the practical implications of having a fast algorithm for the calculation of the density of states of frustrated systems. |
Monday, March 5, 2018 10:12AM - 10:24AM |
A38.00010: Dynamic scaling in the two-dimensional Ising spin glasses Na Xu, Kai-Hsin Wu, Shanon Rubin, Ying-Jer Kao, Anders Sandvik We carry out simulated annealing and employ a generalized Kibble-Zurek (KZ) scaling hypothesis to study the 2D Ising spin glass with normal-distributed couplings [1]. From a scaling analysis when T→0 at different annealing velocities v, we find power-law scaling in the system size for the velocity required in order to relax toward the ground state; v∼ L-(z+1/ν), where z is the dynamic exponent. We find z ≈13.6 for both the Edwards-Anderson order parameter and the excess energy. This is different from a previous study with bimodal couplings, where the dynamics is faster and the above two quantities relax with different dynamic exponents [2]. Our results reinforce the conclusion of anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the case of a continuous coupling distribution, our results also indicate that, although KZ scaling holds, the perturbative behavior normally applying in the slow limit breaks down, likely due to quasi-degenerate states, and the scaling function takes a different form. |
Monday, March 5, 2018 10:24AM - 10:36AM |
A38.00011: Dynamic scaling of topological ordering in classical systems Na Xu, Claudio Castelnovo, Roger Melko, Claudio Chamon, Anders Sandvik We analyze scaling behaviors of simulated annealing carried out on various classical systems with topological order, obtained as appropriate limits of the toric code in 2D and 3D. We first consider the 3D Ising lattice gauge model, which exhibits a continuous topological phase transition at finite temperature. We show that a generalized Kibble-Zurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeter-law scaling of the magnitude of a non-local order parameter (defined using Wilson loops) and a dynamic exponent z = 2.70 ± 0.03. We then study systems where (topological) order forms only at zero temperature—the Ising chain, the 2D Ising gauge model, and a 3D star model (another variant of the 3D Ising gauge model). We show that the Kibble-Zurek theory does not apply in any of these systems. Instead, the dynamics can be understood in terms of diffusion and annihilation of topological defects, which we use to formulate a scaling theory in good agreement with our simulation results. We also discuss the effect of open boundaries where defect annihilation competes with a faster process of evaporation at the surface. |
Monday, March 5, 2018 10:36AM - 10:48AM |
A38.00012: Combined Molecular and Spin Dynamics Simulation of BCC Iron with Defects Mark Mudrick, Markus Eisenbach, Dilina Perera, David Landau Using an atomistic model that handles translational and spin degrees of freedom, combined molecular and spin dynamics simulations have been performed to study BCC iron containing vacancy defects. Atomic interactions are described by an empirical many-body potential while spin interactions are handled by a Heisenberg-like coordinate dependent exchange interaction. We analyze space-displaced, time-displaced correlation functions to investigate phonon and magnon excitations[1]. We show that the introduction of randomly distributed vacancies causes a decrease in magnon frequency as well as a broadening of the excitation peaks[2]. We show that clustered vacancy defects induce novel excitation modes which are localized within the vicinity of the defect, becoming more distinct from bulk excitations with increasing defect size. |
Monday, March 5, 2018 10:48AM - 11:00AM |
A38.00013: Hybrid Monte Carlo simulations of finite-temperature properties of solids. Sergei Prokhorenko, Kruz Kalke, Yousra Nahas, laurent bellaiche Monte Carlo (MC) algorithms constitute one of the cornerstone numerical frameworks of modern statistical physics. In contrast to molecular or spin dynamics (MD or SD), MC techniques are free of the realistic relaxation time scales and are meant to offer better estimates of "quai-static" thermodynamic averages at equilibrium. However, popular MC algorithms lack of scalable parallelization strategy for systems with long-range interactions and cannot be readily used for ab intio structural relaxation. Hybrid Monte Carlo algorithm (HMC) offers a straightforward solution to this drawback by incorporating MD into the random trial state generator. Surprisingly, despite its popularity in computational lattice field theory, the applications of HMC in the context of structural and spin dynamics are hard to find. In this study, we present an open-source HMC code for ultra-large-scale effective Hamiltonian simualtions and an implementation of HMC algorithm within Abinit software suite. We then present computational benchmarks and reveal advantages of this algorithm. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700