Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z49: Computational Methods for Statistical Mechanics: Advances and Applications IFocus Recordings Available

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Sponsoring Units: DCOMP GSNP Chair: Alfred Farris, Emory University Room: McCormick Place W471B 
Friday, March 18, 2022 11:30AM  12:06PM 
Z49.00001: Parallel flathistogram method for equilibrium and nonequilibrium problems Invited Speaker: Johannes Zierenberg I will present a parallel implementation of the multicanonical method and its generalization to a flathistogram method suitable for other equilibrium ensembles as well as nonequilibrium problems. After a tutorial introduction to the method, I will present several successful applications to diverse equilibrium problems, both on and offlattice, and new applications to spreading processes. 
Friday, March 18, 2022 12:06PM  12:18PM 
Z49.00002: Microcanonical InflectionPoint Analysis of Phases for Semiflexible Polymers Dilimulati Aierken, Michael Bachmann We study a generic model of semiflexible polymer with selfinteractions, which is known to exhibit a multitude of structural phases. Previous studies employing canonical statistical analysis methods for the identification and characterization of these phases have been inconclusive as these approaches lead to inconsistent results for systems of finite size. For our study, we use the recently introduced generalized microcanonical inflectionpoint analysis method [1]. This analysis technique was developed to enable the systematic identification and classification of transitions in systems of any size. In this talk, we discuss the structural hyperphase diagram of semiflexible polymers in the range of comparatively large bending stiffness, which extends a previous case study [2]. Extensive replicaexchange Monte Carlo simulations were performed to obtain accurate estimates of the microcanonical entropies for the different values of the bending stiffness. 
Friday, March 18, 2022 12:18PM  12:30PM 
Z49.00003: Statistical Mechanics of Chemical Disorder and Magnetic Order in MnSb_{2}Te_{4} and MnBi_{2}Te_{4} Markus Eisenbach, Swarnava Ghosh, MaoHua Du, Mina Yoon, Fernando A Reboredo The magnetic ordering in the layered topological insulator materials MnSb_{2}Te_{4} and MnBi_{2}Te_{4} has been observed to depend strongly on the disorder and defects on the Mn and Sb/Bi sublattices. Here we will explore the effect of this chemical disorder on the magnetic interactions and we will present models of the magnetic interactions in these materials that have been extracted from large scale first principles density functional theory calculations. The first principles calculations consider unbiased disorder realizations to capture the magnetic interactions both inside the planes as well as between planes based on the chemical environment. These models form the basis for our MonteCarlo simulations where we identify the magnetic transitions between the ferromagnetic and antiferromagetic states as a function of disorder as well as the transition temperatures for these magnetic orders. 
Friday, March 18, 2022 12:30PM  12:42PM 
Z49.00004: A graph theorybased statistical mechanics approach for nucleation of nanoporous materials Ajay Muralidharan, Xinyi Li, J.R. Schmidt Understanding the nucleation of weak electrolytes from solution is critical for the design and synthesis of crystalline nanoporous materials such as metalorganic frameworks (MOFs) and zeolites. However, existing simulation approaches to model nucleation are often extremely limited when applied to weak electrolytes. We developed a novel graph theorybased sampling approach that overcomes limitations of existing approaches, especially, for bulk solvent systems. Our method seeks to exploit the property of materials whose crystal structure exhibit directional bonding and thus can be described as a "graph" of connected monomers. By utilizing a rigorous statisticalmechanics approach, we generate a nucleus of size N+1 from size N by performing a Monte Carlo type attachment of a solute to the surface of a nucleus followed by a thermodynamic integration step to turn on interactions. A "bootstrapping" approach in the nucleus size (N) is then used to generate an ensemble of representative nuclei and their corresponding free energies. To validate our approach, we begin with an ideal system of non interacting particles and evaluate the free energy dependence with nucleus size. The free energies show excellent agreement with reference values obtained from a GCMC (Grand Canonical Monte Carlo) approach. Subsequent work will extended our approach to treat systems with more complex interactions and geometries. 
Friday, March 18, 2022 12:42PM  12:54PM 
Z49.00005: Testing and Usage of an Automated Multibead Iterative Boltzmann Inversion (IBI) Code Lilian C Johnson, Frederick R Phelan Iterative Boltzmann Inversion (IBI) is a systematic coarsegraining (CG) method in which tabular CG potentials are derived that reproduce target distributions generated from atomistic reference simulations. We report here on a software code which automates the development of multibead coarsegrained potentials using IBI. Two major problems make automation difficult: 1) noisy distributions derived from sampling; 2) low sampling regions which introduces discontinuities in the sampling. Both of these make differentiation to calculate energy and forces difficult and error prone. Our code addresses these problems using an approach which combines data smoothing, fitting to functional expansions, and extrapolation schemes to handle low sampling regions without discontinuity or data distortion. A number of code features will be discussed aimed at providing guidance on usage. In particular, we discuss the importance of proper sampling and equilibration in the reference simulations and how this leads accurate target distributions in low sampling regions (as well as the suppression of erroneous features) which is a key to potential convergence. Finally, we discuss associated tools that enable robust input including automated conversion of molecular systems from allatom (AA) to CG models. 
Friday, March 18, 2022 12:54PM  1:06PM 
Z49.00006: Fitting Hamiltonian Parameters with Bayesian Optimization of Numerical Simulations Matthew S Wilson, YingWai Li, Kipton M Barros, Sakib Matin, Cole M Miles, Xiaojian Bai, Martin P Mourigal, Cristian Batista Tuning simulation models to accurately reproduce experimental observations is a challenging but vital task for predicting material properties and informing further experiments. The search for a set of suitable Hamiltonian parameters should ideally minimize the number of dispatched simulations and be fully automated to maximize throughput. We describe a framework that utilizes Bayesian optimization[1], which fits surrogate models predicting the expected difference between target observables and results of numerical simulations, to intelligently explore and optimize in parameter space. The optimization scheme is robust in application and can function without relying on any gradient information. We apply this methodology to Monte Carlo simulations of a coarsegrained binary alloy model to successfully recover a reference interspecies coupling calculated from first principles methods[2]. The Hamiltonian fitting procedure is then demonstrated for experimental data and dynamical simulations of continuous spin models for magnetic materials. 
Friday, March 18, 2022 1:06PM  1:18PM 
Z49.00007: Avoiding critical slowdown in models with SALR interactions Mingyuan Zheng, Marco Tarzia, Patrick Charbonneau Particles with competing shortrange attractive and longrange repulsive (SALR) interactions can form a broad array of microphase morphologies. Given that structural richness, minimal models solved by Monte Carlo methods help to hone in on the underlying physics. However, even at weak frustration, configurational sampling in the vicinity of orderdisorder transition temperature, $T_c$, is particularly inefficient. Standard cluster algorithms, such as the SwendsenWang and Wolff schemes, then fail because they generate clusters that don't capture physical correlations and even percolate at $T>T_c$. Alternate approaches have hence long been sought out. In this presentation, we present a meanfield analysis of this challenge and use our findings to propose an algorithmic approach that sidesteps these difficulties. 
Friday, March 18, 2022 1:18PM  1:30PM 
Z49.00008: Asymptotic Error Analysis of the MBAR Equations Sherry Li The efficient estimation of highdimensional integrals is central to answering many questions in statistical mechanics. An important class of sampling strategies, including umbrella sampling and alchemical methods, involves sampling from multiple thermodynamic states. A statistically optimal estimator named Multistate Bennett Acceptance Ratio (MBAR) has been developed to systematically combine data from all the sampled states to estimate free energies and other ensemble averages over another probability distribution. However, the error of the MBAR estimator is not wellunderstood: previous error analysis of MBAR assumed independent samples and only gave the total error without tracing the error to individual sampled states. In this work, We derive a central limit theorem for the estimates from MBAR, which allows for error decomposition into individual sampled states. We demonstrate the error estimator for a twodimensional umbrella sampling of the alanine dipeptide and the alchemical free energy calculation of the solvation of methane in water. Our error analysis suggests a close connection between error contribution of each state and the autocorrelation in the samples from that state. The preliminary results suggest that assessing the error contributions provides insight into the sources of error of the simulations and can be used to improve the accuracy of MBAR calculations. 
Friday, March 18, 2022 1:30PM  1:42PM 
Z49.00009: Some Numerical Issues in Polymer DensityFunctional Theories for Tangent HardSphere Chains Jiawei Zhang, Baohui Li, Qiang Wang The two most popular polymer densityfunctional theories (PDFTs), one proposed by Yu and Wu (J. Chem. Phys. 117, 2368, 2002) and the other by Chapman and coworkers (J. Chem. Phys. 127, 244904, 2007), are both applicable only to model systems based on tangent hardsphere chains. Due to the hardsphere repulsion, however, many integrals involved in these PDFTs contain discontinuous and/or indifferentiable integrands, and cannot be accurately evaluated by the straightforward application of any quadrature or Fourier transform. Here we show how to solve this problem in both realspace and reciprocalspace calculations, using the later versions of both PDFTs (J. Chem. Phys. 118, 3835, 2003; J. Chem. Theory Comput. 8, 1393, 2012). We also use an iteration method that can converge the PDFT equations to much higher accuracy than the commonly used Picard iteration (also known as the simple mixing or relaxation method). These allow us to obtain highly accurate results (where the maximum absolute value of the residual errors is less than 10^{10}) in much less iteration steps. 
Friday, March 18, 2022 1:42PM  1:54PM 
Z49.00010: LoopCluster Coupling and Algorithm for Classical Statistical Models Lei Zhang Potts spin systems play a fundamental role in statistical mechanics and quantum field theory and can be studied within the spin, the Fortuin–Kasteleyn (FK) bond or the qflow (loop) representation.We introduce a LoopCluster (LC) joint model of bondoccupation variables interacting with qflow variables and formulate an LC algorithm that is found to be in the same dynamical universality as the celebrated Swendsen–Wang algorithm. This leads to a theoretical unification for all the representations, and numerically, one can apply the most efficient algorithm in one representation and measure physical quantities in others. Moreover, by using the LC scheme, we construct a hierarchy of geometric objects that contain as special cases the qflow clusters and the backbone of FK clusters, the exact values of whose fractal dimensions in two dimensions remain as an open question. Our work not only provides a unified framework and an efficient algorithm for the Potts model but also brings new insights into the rich geometric structures of the FK clusters. 
Friday, March 18, 2022 1:54PM  2:06PM 
Z49.00011: Funnel Hopping Monte Carlo: Efficient Monte Carlo simulations for multifunnel systems Jonas A Finkler, Stefan A C Goedecker Monte Carlo simulations are a popular tool used in physics, chemistry and biology to study the behavior of atomic systems at finite temperatures. 
Friday, March 18, 2022 2:06PM  2:18PM 
Z49.00012: Langevin Dynamics Simulations of Dielectric Response of Correlated Materials Steven B Hancock, David P Landau, Yohannes Abate We have developed a fast and flexible computational scheme to calculate the complex valued, frequency dependent dielectric function ε(ω) of correlated materials. The premise of such a methodology is to use the atomistic crystal structure of materials and designate relatively simple bond length and bondangle interactions, as well as internal field couplings to accommodate correlation. Once these interactions are appropriated, we simulate systems of N x N x M unit cells with periodic boundary conditions via Langevin dynamics under an oscillating external electric field. We validate our method by recreating highresoltuion infrared nearfield experimental results of the dielectric function of perovskite oxide SmNiO_{3}. We show quantitative agreement with experimental data concerning the modulation of the nanoscale dielectric changes as a function of hydrogen doping and the prevalence of oxygen vacancies within the sample. We also show representative example of how our methodology can gain us nanoscale insight into the dielectric behavior of Moire patterned twodimensional transition metal dichalcogenides and compare our results with highresolution nearfield measurements. 
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