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Sampling vacancy configurations with large relaxations using Smart Darting

Physical Review Materials 2024年第3期8卷 033604-033604页

作者： D. Tanguy Université Lyon Université Claude Bernard Lyon 1 CNRS Institut Lumière Matière Villeurbanne F-69622 France

Markov chain Monte Carlo simulations, combining the sampling of the position of the particles and their chemical nature, are very useful when calculating, for example, average site occupancies at crystalline defects in alloys. Unfortunately, when the relaxations around the solutes are large, the exchange moves can be systematically rejected because of atoms overlapping. As a consequence, the simulations are often trapped in nonphysical configurations. In this paper, the “Smart Darting” method from Andricioaei et al. is adapted and extended to propose a solution to this limitation. The method is tested in a particularly demanding case: the sampling of the arrangements of delocalized vacancies and divacancies in grain boundaries, both in the fcc and the bcc structure. Beyond the methodological aspects, intergranular vacancy clusters are interesting in several contexts, such as ductile fracture, irradiation, or thin-film dewetting, and therefore several properties have been measured that can be useful for mesoscale modeling: segregation energies, effective diffusion barriers in and out of the grain boundaries, vacancy-vacancy binding energies, and elastic dipole tensors.

关键词： Fracture Grain boundaries Point defects Self-diffusion metropolis algorithm

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Monte Carlo spin simulations of magnetic noise: The search for pivoting

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Physical Review B 2024年第14期109卷 144510-144510页

作者： D. L. Mickelsen Ruqian Wu Clare C. Yu Department of Physics and Astronomy University of California Irvine California 92697 USA

Superconducting quantum interference devices (SQUIDs) show great promise as quantum bits (qubits) but continue to be hindered by flux noise. The flux noise power spectra of SQUIDs go as 1/fα, where α is the temperature-dependent noise exponent. Experiments find 0.5≲α≲1. Furthermore, experiments find that the noise power spectra versus frequency at different temperatures pivot about or cross at a common point for each SQUID. To try to better understand the results and motivated by experimental evidence that magnetic moments on the surface of SQUIDS produce flux noise, we present the results of our Monte Carlo simulations of various spin systems on 2D lattices. We find that only spin glasses produce α∼1 at low temperature. We find that aliasing of the noise power spectra at high frequencies can lead to spectral pivoting if it is in proximity to a knee at a slightly lower frequency. We show that the pivot frequency depends on the method of site selection and how often the magnetization is recorded. The spectral pivoting that occurs in our simulations is due to aliasing and does not explain the spectral pivoting of experiments.

关键词： Superconductors XY model Antiferromagnets Ferromagnets SQUID Spin glasses Superconducting qubits metropolis algorithm Monte Carlo methods

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Statistical mechanical model for crack growth

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Physical Review E 2024年第1期109卷 015001-015001页

作者： Michael R. Buche Scott J. Grutzik Computational Solid Mechanics and Structural Dynamics Sandia National Laboratories Albuquerque New Mexico 87185 USA Materials and Failure Modeling Sandia National Laboratories Albuquerque New Mexico 87185 USA

Analytic relations that describe crack growth are vital for modeling experiments and building a theoretical understanding of fracture. Upon constructing an idealized model system for the crack and applying the principles of statistical thermodynamics, it is possible to formulate the rate of thermally activated crack growth as a function of load, but the result is analytically intractable. Here, an asymptotically correct theory is used to obtain analytic approximations of the crack growth rate from the fundamental theoretical formulation. These crack growth rate relations are compared to those that exist in the literature and are validated with respect to Monte Carlo calculations and experiments. The success of this approach is encouraging for future modeling endeavors that might consider more complicated fracture mechanisms, such as inhomogeneity or a reactive environment.

关键词： Classical statistical mechanics Growth processes Thermodynamics Continuum particle models Lattice models in statistical physics Approximation methods for many-body systems Many-body techniques metropolis algorithm Monte Carlo methods Numerical approximation & analysis

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Three-dimensional Heisenberg model with Dzyaloshinskii-Moriya interaction: A Monte Carlo study

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Physical Review E 2024年第6期109卷 064113-064113页

作者： G. Albuquerque Silva A. R. Bergeron J. A. Plascak D. P. Landau Departamento de Física Instituto de Ciências Exatas Center for Simulational Physics The Centro de Ciências Exatas e da Natureza–Campus I Departamento de Física–CCEN Cidade Universitária 58051-970 João Pessoa PB Brazil

The three-dimensional classical Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions between nearest-neighbors in all directions has been studied using Monte Carlo simulations. The metropolis algorithm, combined with single histogram reweighting techniques and finite-size scaling analyses, has been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Simulations were performed with the same set of interaction parameters for both shifted boundary conditions (SBC) and fluctuating boundary conditions (FBC). Because of an incommensurability caused by the DM interaction, the SBC incorporated a fixed shift angle at the boundary which varies as a function of the DM interaction and lattice size. This SBC method decreases the simulation time significantly, but the distribution of states is somewhat different than that obtained with FBC. The ground state for nonzero DM interaction is a spiral configuration where the spins are restricted to lie in planes perpendicular to the DM vector. We found that this spiral configuration undergoes a conventional second-order phase transition into a disordered, paramagnetic state with the transition temperature being a function of the magnitude of the DM interaction. The limiting case with only DM interaction in the model has also been considered. The critical exponent ν, the critical exponent ratios α/ν, β/ν, γ/ν, as well as the critical temperature Tc and fourth-order cumulant of the order parameter U4* at Tc have been estimated for different magnitudes of DM interaction. The critical exponents and cumulants at the transition are different from those for the three-dimensional Heisenberg model, but the ratios α/ν, β/ν, γ/ν, U4*/ν are the same, implying that weak universality is valid for all values of DM interaction. Structure factor calculations for particular cases have been performed considering SBC and FBC in the simulations with different lattice sizes at the critical t

关键词： Classical statistical mechanics Critical phenomena Phase transitions Classical spin models Lattice models in statistical physics metropolis algorithm Monte Carlo methods

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Enhanced Sampling of Configuration and Path Space in a Generalized Ensemble by Shooting Point Exchange

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Physical Review Letters 2024年第12期132卷 128001-128001页

作者： Sebastian Falkner Alessandro Coretti Christoph Dellago University of Vienna Faculty of Physics 1090 Vienna Austria.

The computer simulation of many molecular processes is complicated by long timescales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path sampling with enhanced exploration of configuration space. The method relies on exchange moves between configuration and trajectory space, carried out based on a generalized ensemble. This scheme substantially enhances the efficiency of the transition path sampling simulations, particularly for systems with multiple transition channels, and yields information on thermodynamics, kinetics and reaction coordinates of molecular processes without distorting their dynamics. The method is illustrated using the isomerization of proline in the KPTP tetrapeptide.

关键词： Biomolecular dynamics Stochastic processes Thermodynamics Biomolecules Peptides Langevin algorithm metropolis algorithm Molecular dynamics Monte Carlo methods

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Island density scaling in reversible submonolayer growth with attachment barriers

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Physical Review E 2024年第3期109卷 034803-034803页

作者： Oliver Smirnov Jacques G. Amar Department of Physics & Astronomy University of Toledo Toledo Ohio 43606 USA Department of Physics Columbia University New York New York 10027 USA

Island nucleation and growth play an important role in thin-film growth. One quantity of particular interest is the exponent χ, which describes the dependence of the saturation island density Nsat∼(Dh/F)−χ on the ratio Dh/F of the monomer hopping rate Dh to the deposition rate F. While standard rate equation (RE) theory predicts that χ=i/(i+2) (where i is the critical island size), more recently it has been predicted that in the presence of a strong barrier to the attachment of monomers to islands, a significantly larger value χ=2i/(i+3) may be observed. While this prediction has recently been tested using kinetic Monte Carlo simulations for the case of irreversible growth corresponding to i=1, it has not been tested for the case of reversible island growth corresponding to i>1. Here we present a mean-field self-consistent RE method which we have used to study the dependence of the effective value of χ on Dh/F and barrier-strength for i=1,2,3, and 6. Both the no-nucleation-barrier case in which there exists a barrier for monomers to attach to islands larger than the critical island size (but not to smaller islands) and the nucleation-barrier case in which there is a barrier for monomers to attach to islands of all sizes are studied. In all cases, we find that the existence of attachment barriers significantly increases the effective value of χ for a given barrier strength. In addition, for i=1 we find good agreement between our extrapolated asymptotic value of χ and the theoretical strong-barrier prediction both with and without a nucleation barrier. In contrast, for i>1 the value of χ is significantly larger in the presence of a nucleation barrier than in its absence. In particular, while an asymptotic analysis of our results for i>1 also leads to excellent agreement with the strong barrier prediction in the presence of a nucleation barrier, in the absence of a nucleation barrier the asymptotic values are significantly lower.

关键词： Island Nucleation on surfaces Monolayer films Vacuum interfaces Materials modeling Mean-field & cluster methods metropolis algorithm Physical vapor deposition

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Equilibrium structure of 1,4-cyclohexadiene monolayer on Si(001)-(2 × 1)

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Physical Review B 2024年第4期110卷 045416-045416页

作者： V. A. Gorbunov A. I. Uliankina S. S. Akimenko A. V. Myshlyavtsev Department of Chemistry and Chemical Engineering

The adsorption layer of 1,4-cyclohexadiene on Si(001)-(2 × 1) is one of the most studied organic/semiconductor interfaces. To this day the stable structure of the adsorption layer and its dependence on pressure and temperature are hypothetical. In this work, we have developed several lattice models of the adsorption layer of 1,4-cyclohexadiene (1,4-CHD) on Si(001)-(2 × 1), taking into account the main features of the chemisorbed layer: different types of adsorption complexes and their asymmetry, and repulsive intermolecular interactions. A unique combination of density functional theory methods and the tensor renormalization group within the framework of the developed models allowed us to reveal the equilibrium structure of 1,4-CHD monolayer on the Si(001)-(2 × 1) surface. We have found four stable phases in the most advanced model. There are two phases consisting of tetra-bound (tetra-σ) complexes only: the phase of mixed composition with tetra-bound and double-bound (di-σ) complexes, and the close-packed phase, where each Si=Si dimer of the Si(001)-(2 × 1) surface is occupied by a di-σ complex. All the phases differ in the number of 1,4-CHD molecules per Si=Si dimer. Repulsive intermolecular interactions along the row of Si=Si dimers are demonstrated to determine the self-assembly of two phases. Those are the phase of the lowest density that comprises only the tetra-bound complexes and the phase of mixed composition. Repulsion between 1,4-CHD molecules adsorbed on neighboring rows of Si=Si dimers leads to a coordinated filling of these rows. As a result, the existence region of the mixed phase consisting of the tetra-σ and di-σ complexes narrows. The transition from the phase consisting of tetra-bound complexes to the phase of mixed composition is found to occur abruptly through a first-order phase transition.

关键词： Adsorption Interface & surface thermodynamics Equilibrium lattice models Semiconductors Solid-gas interfaces Density functional theory metropolis algorithm Tensor network methods Tensor network renormalization Transfer matrix method

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Exact equilibrium properties of square-well and square-shoulder disks in single-file confinement

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Physical Review E 2024年第2期110卷 024601-024601页

作者： Ana M. Montero Andrés Santos Departamento de Física Universidad de Extremadura E-06006 Badajoz Spain Instituto de Computación Científica Avanzada (ICCAEx) Universidad de Extremadura E-06006 Badajoz Spain

This study investigates the (longitudinal) thermodynamic and structural characteristics of single-file confined square-well and square-shoulder disks by employing a mapping technique that transforms the original system into a one-dimensional polydisperse mixture of nonadditive rods. Leveraging standard statistical-mechanical techniques, exact results are derived for key properties, including the equation of state, internal energy, radial distribution function, and structure factor. The asymptotic behavior of the radial distribution function is explored, revealing structural changes in the spatial correlations. Additionally, exact analytical expressions for the second virial coefficient are presented. The theoretical results for the thermodynamic and structural properties are validated by our Monte Carlo simulations.

关键词： Confinement Hard sphere colloids metropolis algorithm

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Interplay between Markovianity and progressive quenching

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Physical Review E 2024年第3期109卷 034106-034106页

作者： Charles Moslonka Ken Sekimoto Laboratoire Gulliver UMR CNRS 7083 ESPCI Paris 75005 Paris France Laboratoire Matière et Systèmes Complexes UMR CNRS 7057 Université Paris Cité 75013 Paris France

Progressive quenching (PQ) is a process in which we sequentially fix a system's degrees of freedom, which would otherwise evolve according to their stochastic dynamics. Previous studies have discovered what we refer to as the hidden martingale property in PQ. Here we first attribute this martingale property to the canonicity of the two-layer ensemble comprising quenched and thermal ensembles and demonstrate that the Markovian property, coupled with the detailed balance (DB) of the evolution dynamics, underpins this canonicity. We then expand the PQ to the Markovian dynamics on the transition network where the DB is not required. Additionally, we examine the PQ of the systems that evolve through non-Markovian dynamics between consecutive quenching. When non-Markovian dynamics ensure a trajectory-wise DB, such as in an equilibrium spin system with a hidden part, the PQ can occasionally maintain the canonical structure of the overall statistical ensemble but not always. Last, we analytically and numerically investigate the PQ of a non-Markovian spin system with delayed interaction and illustrate how the reduction of spin correlations due to the delay can be compensated by the PQ.

关键词： Nonequilibrium statistical mechanics Stochastic processes Stochastic thermodynamics Classical spin models Ising model Markovian processes metropolis algorithm Non-Markovian processes Transfer matrix calculations

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PERFORMANCE OF THE metropolis algorithm ON A DISORDERED TREE: THE EINSTEIN RELATION

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ANNALS OF APPLIED PROBABILITY 2014年第5期24卷 2070-2090页

作者： Maillard, Pascal Zeitouni, Ofer Weizmann Inst Sci Dept Math & Comp Sci IL-76100 Rehovot Israel

Consider a d-ary rooted tree (d >= 3) where each edge e is assigned an i.i.d. (bounded) random variable X (e) of negative mean. Assign to each vertex v the sum S(v) of X (e) over all edges connecting v to the root, and assume that the maximurn S-n* of S(v) over all vertices v at distance n from the root tends to infinity (necessarily, linearly) as n tends to infinity. We analyze the metropolis algorithm on the tree and show that under these assumptions there always exists a temperature 1/beta of the algorithm so that it achieves a linear (positive) growth rate in linear time. This confirms a conjecture of Aldous [algorithmica 22 (1998) 388-412]. The proof is obtained by establishing an Einstein relation for the metropolis algorithm on the tree.

关键词： metropolis algorithm Einstein relation branching random walk random walk in random environment

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