Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session A38: Advances in Computational Statistical Mechanics and their Applications: Part 1Focus

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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: Duality and conditional expectations in the NakajimaMoriZwanzig formulation Jason Dominy , Daniele Venturi We develop a new operator algebraic formulation of the NakajimaMoriZwanzig (NMZ) method of projections. The new theory is built upon rigorous mathematical foundations, and it can be applied to both classical and quantum systems. We show that a duality principle between the NMZ formulation in the space of observables and in the state space can be established, analogous to the Heisenberg and Schrodinger pictures in quantum mechanics. Based on this duality we prove that under natural assumptions, the projection operators appearing in the NMZ equation must be conditional expectations. The proposed formulation opens the way to novel computational approaches in coarsegrained dynamics of highdimensional systems, and is illustrated with analytic and numerical examples. 
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 32bit and 53bit 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 16^{3} to 1024^{3}. By analyzing data with crosscorrelations [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 K_{c} = 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 clusterflip relaxations in Ising models Yusuke Tomita , Yoshihiko Nonomura At critical points, powerlaw relaxations are ubiquitously observed. In Monte Carlo simulations using localupdate, the understanding of the relations between dynamical and critical exponents enable us to study critical phenomena by observing their powerlaw relaxations. On the other hand, little is known about relaxations in clusterflip updates. Recently Nonomura claimed that critical nonequilibrium relaxation of the 2dimensional Ising model by clusterflip update is described by the stretchedexponential type [1]. Furthermore our consecutive studies confirmed that the stretchedexponential relaxation is ubiquitous in clusterflip Monte Carlo simulations [2,3]. To understand the origin of the relaxation, we analyse the 2, 3, 4dimensional, and infiniterange Ising models. While the infiniterange Ising model shows the simple exponential relaxation, the stretchedexponential 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 antiferromagneticlike shortrange 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 shortrange (SR) interactions [1]. In this model, the interplay between the SR interaction and the longrange (LR) interaction of elastic origin causes complex phase transitions. For relatively weak elastic interactions, the phase diagram is characterized by tricritical points, at which AFlike 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 Flike 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 infiniterange 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 dephase quantum states and classical simulations become accurate. Here, detailed comparisons are made to many spin networks and quantumclassical 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: Studying phase transitions by zeros in energy probability distribution Invited Speaker: Bismarck Costa , Lucas M\'ol , J\'ulio Rocha , Lucas Menicucci We describe an iterative method to study the critical behavior of a system based on the partial knowledge of the complex zeros set of the partition function. The method is general with advantages over most conventional techniques since it does not need to identify any order parameter a priori. The critical temperature and exponents can be obtained with great precision with a low computer time cost. To test the method and to show how it works we applied it to several models with first order, continuous and BKT transitions. Two examples, one with two transitions and other with a bicritical point are also presented. The strategy can easily be adapted to any model, classical or quantum, once we can build the corresponding energy probability distribution. 
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 shortrange interactions one can use domain decompositions for parallel updates. A complementary approach simulates several chains in parallel, either at different temperatures such as in replicaexchange 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 10^{5} 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 freeenergy 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 stateoftheart 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 firstexcited 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 twodimensional Ising spin glasses Na Xu , KaiHsin Wu , Shanon Rubin , YingJer Kao , Anders Sandvik We carry out simulated annealing and employ a generalized KibbleZurek (KZ) scaling hypothesis to study the 2D Ising spin glass with normaldistributed couplings [1]. From a scaling analysis when T→0 at different annealing velocities v, we find powerlaw 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 EdwardsAnderson 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 entropydriven 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 quasidegenerate 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 KibbleZurek scaling ansatz applies to this transition, in spite of the absence of a local order parameter. We find perimeterlaw scaling of the magnitude of a nonlocal 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 KibbleZurek 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 manybody potential while spin interactions are handled by a Heisenberglike coordinate dependent exchange interaction. We analyze spacedisplaced, timedisplaced 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 finitetemperature 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 "quaistatic" thermodynamic averages at equilibrium. However, popular MC algorithms lack of scalable parallelization strategy for systems with longrange 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 opensource HMC code for ultralargescale effective Hamiltonian simualtions and an implementation of HMC algorithm within Abinit software suite. We then present computational benchmarks and reveal advantages of this algorithm. 
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