Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session V22: Computational Methods for Statistical Mechanics: Advances and Applications  IIFocus Live

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Sponsoring Units: DCOMP GSNP Chair: Alfred Farris, Emory University 
Thursday, March 18, 2021 3:00PM  3:36PM Live 
V22.00001: Efficient Simulation of SelfAvoiding Walks Invited Speaker: Nathan Clisby Selfavoiding walks are simply defined as walks on a lattice that avoid themselves, and provide the simplest model of a polymer that captures universal features such as the Flory exponent ν which characterises the size of a polymer. In recent years, high precision Monte Carlo simulations of selfavoiding walks with many millions of steps have been realised through the use of a radically efficient implementation of the pivot algorithm via a hierarchical data structure. This data structure allows for global updates of the system to be performed in the same CPU time as local updates. 
Thursday, March 18, 2021 3:36PM  3:48PM Live 
V22.00002: Deriving LBM Collision Operator using the CoarseGraining MDLG Approach Aleksandra Pachalieva, Alexander Wagner The MolecularDynamicsLatticeGas (MDLG) method by Parsa et. al [1] establishes a direct link between a lattice gas method and the coarsegraining of a Molecular Dynamics (MD) approach. Due to its connection to MD, the MDLG rigorously recovers the hydrodynamics and allows to validate the behavior of the Lattice Gas (LG) or Lattice Boltzmann Methods (LBM) without using the standard kinetic theory approach. This MDLG analysis tool has the potential to verify and examine the properties of the LG and the LBM methods for fluctuating, thermal, multiphase and multi component systems. 
Thursday, March 18, 2021 3:48PM  4:00PM Live 
V22.00003: Multithermalmultibaric ensembles from collectivevariablesbased enhanced sampling methods Pablo Piaggi, Michele Invernizzi, Thomas Edward Gartner, Haiyang Niu, Michele Parrinello Thermodynamic ensembles that exist in nature are usually characterized by some constraint such as having constant energy or temperature. Computer simulations are not only able to reproduce these ensembles but they are also capable of creating new ensembles with different characteristics. Generalized ensembles such as the multicanonical ensemble have been shown to improve the sampling of rugged free energy landscapes and phase transitions. A natural extension is the multithermalmultibaric ensemble in which a large region of the temperature and pressure phase diagram can be sampled in a single simulation. We will discuss two methods to generate multithermalmultibaric ensembles using the potential energy and the volume as collective variables to construct a bias potential. We have employed these algorithms to study the folding of the miniprotein chignolin and to obtain evidence of a liquidliquid transition in a model of water. Furthermore, we have extended this approach to seamlessly integrate the sampling of a kinetic bottleneck through the addition of one or more collective variables that describe slow modes of the system. We have applied this method successfully to the calculation of liquidsolid phase diagrams in sodium, aluminum, and gallium. 
Thursday, March 18, 2021 4:00PM  4:12PM Live 
V22.00004: NonReversible Monte Carlo Simulations of LongRange Interacting Molecular Systems Philipp Hoellmer, Liang Qin, Michael F. Faulkner, A. C. Maggs, Werner Krauth We present current progress of developing nonreversible Markovchain Monte Carlo (MCMC) algorithms for efficient simulations of atombased models of molecules that include longranged interactions. The eventchain Monte Carlo (ECMC) algorithm samples the Boltzmann distribution exactly without computing energy changes, which removes the computational bottleneck of traditional reversible MCMC simulations. Also, in contrast to molecular dynamics, the mixing and autocorrelation times of MCMC are not locked to the physical dynamics. 
Thursday, March 18, 2021 4:12PM  4:24PM Live 
V22.00005: Measuring configurational entropy of glasses using population annealing Chris Amey, Jonathan Lee Machta In this talk we present two methods to calculate the vibrational (S_{vib}) and configurational (S_{c}) entropies of glassy fluids in the context of population annealing Monte Carlo. The first method for obtaining S_{vib} integrates the pressure of individual configurations from the fluid phase to the glass phase, and the second method introduces a hard shell constraining potential to individual particles at fixed packing fraction in the glassy regime and integrates the entropy to the highly constrained, ideal gas limit. Using population annealing, we obtain measurements of S_{vib} and S_{c} at high densities for fluids with 30, 60, and 100 particles and compare the two methods. Our results show that the two methods agree and that even for modestsized systems, finitesize effects on S_{c} appear to be small. 
Thursday, March 18, 2021 4:24PM  4:36PM Live 
V22.00006: Parallel multicanonical simulations applied to equilibrium cluster formation Johannes Zierenberg Cluster formation occurs in supersaturated or supercooled solutions and involves a large freeenergy barrier. For equilibrium systems in the canonical ensemble, this freeenergy barrier diverges with system size. Such problems that involve large freeenergy barriers can be efficiently studied with flathistogram MonteCarlo algorithms that artificially enhance the probability of otherwise suppressed states. One particular flathistogram algorithm is the multicanonical method, where an auxiliary weight function is iteratively adapted to produce a flat histogram. The beauty of this approach is that each iteration samples from an equilibrium distribution due to fixed weights, such that this process can be parallelized very easily and very efficiently. We will present in detail this parallel scheme for CPU and GPU architectures and show its closetoperfect scaling up to 10k threads. In addition, we present recent applications using parallel multicanonical simulations to study cluster formation in particle and polymer systems, reaching previously inaccessible scaling regimes. 
Thursday, March 18, 2021 4:36PM  4:48PM Live 
V22.00007: Error bars for Markov chain Monte Carlo data streams Jonathan Moussa Error bars are typically assigned to Markov chain Monte Carlo data by either an uncorrelated analysis of blockaveraged data or a truncated summation of the autocorrelation function. These analysis methods depend on a choice of either a block size or a truncation point in addition to a choice of equilibration point separating equilibrated from unequilibrated data. In this talk, we present a hierarchical analysis method combining block averaging and autocorrelation summation that efficiently determines the equilibration and truncation points to a predetermined relative precision. Furthermore, we implement this method to accommodate the input of arbitrarily partitioned data streams and the output of error bars on demand. 
Thursday, March 18, 2021 4:48PM  5:00PM Live 
V22.00008: Algorithm for the replica redistribution for population annealing method Alexander Russkov, Roman Chulkevich, Lev Shchur The population annealing method is one of the promising approaches for large scale simulations as potentially scalable on any parallel architecture. We present an implementation of the algorithm on the hybrid program architecture combining CUDA and MPI. The problem is to keep all generalpurpose graphics processing unit devices as busy as possible, redistributing replicas efficiently. We provide details of the testing on Intel Skylake/Nvidia V100 based hardware running in parallel more than two million replicas of the Ising model sample. The results are quite optimistic because the acceleration grows toward the perfect line with the simulated system's growing complexity. 
Thursday, March 18, 2021 5:00PM  5:12PM Live 
V22.00009: Simulating Frustrated Spin Systems with Memory Dynamics Yan Ru Pei, Massimiliano Di Ventra A variety of frustrated lattices have been proposed as models of physical systems and benchmarks for quantum annealers by virtue of their lowtemperature complexity. Standard computational methods for their simulation are inefficient due to the presence of a lowtemperature spinglass phase. For Glaubertype algorithms, the spinflip dynamics are not sufficiently correlated to address the aging of the lattice; for cluster algorithms, the percolation probability is generally above the critical threshold at low temperature. We provide a novel approach, based on the memcomputing architecture, to study these frustrated lattices. This approach features a continuous relaxation of spins, and a correlated memory capable of learning the frustration of the system. This gives rise to longrange dynamics similar to classical cluster updates, without ever employing any algorithmic step. We propose a theoretical model for studying the longrange memory, and a numerical method for its simulation. The simulation results in a polynomialscaling of the relaxation time on the tiling lattice with respect to the system size (while other methods scale exponentially). Finally, we discuss possible extensions to the simulation of quantum systems and general graph structures. 
Thursday, March 18, 2021 5:12PM  5:24PM Live 
V22.00010: A coarsegrained approach to modeling Brownian motion in multidimensional rough potentials Thomas Gray, Ee Hou Yong Diffusion in onedimensional, spatially rough energy landscapes is treated using Zwanzig's formalism, which is based upon the Smoluchowski Equation. With relatively long periods of time spent around the minima interrupted by quick transitions to neighbouring wells, the motion is reminiscent of a particle hopping between sites on a lattice. A CoarseGrained simulation scheme based upon mean firstpassage times and hopping probabilities is introduced and good agreement with Brownian dynamics simulations and theoretical predictions is observed. Extending Zwanzig's formalism to higher dimensions, we derive an expression for the effective diffusion coefficient. From this we obtain expressions for the mean firstpassage time and hopping probabilities, and thereby extend our CoarseGrained scheme to higher dimensions. Again, our scheme is found to replicate the results of Brownian dynamics simulations, which coincide with our theoretical predictions. We conclude by simulating motion in twodimensional disordered potential energy landscapes, where analytic results are difficult to obtain. 
Thursday, March 18, 2021 5:24PM  5:36PM Live 
V22.00011: Probing predictions due to the nonlocal interface Hamiltonian: Monte Carlo simulations of interfacial fluctuations in Ising films Lijun Pang, David P Landau, Kurt Binder Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semiinfinite system. We studied an L × L × D slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localizationdelocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness D. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for D > 6 lattice spacings. 
Thursday, March 18, 2021 5:36PM  5:48PM Live 
V22.00012: Calculating Transport Coefficients from Biased Molecular Dynamics Ernesto Carlos Cortes Morales, Jonathan Whitmer Molecular simulation is a fantastic tool for understanding the link between atomic details and macroscopic properties. Determination of transport properties remains a challenge, due to the long time scales needed to obtain convergent results in commonly used methods, such as equilibrium molecular dynamics simulations combined with the GreenKubo (GK) formalism. The long timescales over which autocorrelation functions must be measured for GK is especially exacerbated when dynamics are slow due to molecular complexity or proximity to a glass transition. Here, we explore the longtime behavior of transport properties by averaging over an ensemble of shorttime trajectories calculated using the GK equation, each reweighting the ensembleaverage by calculating the effective free energy of the local configuration. We explore useful parameters for determining the cutoff time for the short simulations, and methods by which the weight can be efficiently computed. The technique is then applied to calculate shear viscosity for a set of idealized systems, including a KobAndersen mixture prepared near the glassy state. 
Thursday, March 18, 2021 5:48PM  6:00PM Live 
V22.00013: Smart random walks for accelerated Monte Carlo simulations Ying Wai Li, Alfred C. K. Farris, Markus Eisenbach Monte Carlo simulations are robust methods to study statistical physics. However, the unpredictable convergence time and the ease of being trapped in local minima have plagued the efficiency of both traditional and modern Monte Carlo algorithms. We propose strategies to mitigate these problems. We highlight two recent algorithmic developments: the histogramfree multicanonical method for obtaining the density of states for physical systems [1], and a global update scheme that adjusts the sampling weights across the phase space simultaneously. Combining these two methods, we have observed speedups ranging from 13 orders of magnitude compared to existing flathistogram methods such as WangLandau sampling and multicanonical sampling, depending on the problem of interest. These methods are implemented and publicly available in an opensource Monte Carlo software suite, the Oakridge/Opensource WangLandau (OWL) code [2]. 
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