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Constant-pressure nested sampling with atomistic dynamics

Physical Review E 2017年第4期96卷 043311-043311页

作者： Robert J. N. Baldock Noam Bernstein K. Michael Salerno Lívia B. Pártay Gábor Csányi Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL) École Polytechnique Fédérale de Lausanne CH-1015 Lausanne Switzerland Center for Materials Physics and Technology Naval Research Laboratory Washington DC 20375 USA National Research Council Associateship Program resident at the US Naval Research Laboratory Washington DC 20375 USA Department of Chemistry University of Reading Reading United Kingdom Engineering Laboratory University of Cambridge Cambridge United Kingdom

The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are inefficient for condensed systems with general interactions where single-particle moves cannot be evaluated faster than the energy of the whole system. Here we enhance the method by using all-particle moves: either Galilean Monte Carlo or the total enthalpy Hamiltonian Monte Carlo algorithm, introduced in this paper. We show that these algorithms enable the determination of phase transition temperatures with equivalent accuracy to the previous method at 1/N of the cost for an N-particle system with general interactions, or at equal cost when single-particle moves can be done in 1/N of the cost of a full N-particle energy evaluation. We demonstrate this speed-up for the freezing and condensation transitions of the Lennard-Jones system and show the utility of the algorithms by calculating the order-disorder phase transition of a binary Lennard-Jones model alloy, the eutectic of copper-gold, the density anomaly of water, and the condensation and solidification of bead-spring polymers. The nested sampling method with all three algorithms is implemented in the pymatnest software.

关键词： Classical statistical mechanics Entropy Phase behavior Phase diagrams Phase transitions Specific heat Thermal properties Alloys Liquids Molecular solids Entropic sampling methods Hybrid Monte Carlo algorithm metropolis algorithm Molecular dynamics Monte Carlo methods

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J-shaped stress-strain diagram of collagen fibers: Frame tension of triangulated surfaces with fixed boundaries

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Physical Review E 2017年第4期95卷 042411-042411页

作者： Yu Takano Hiroshi Koibuchi National Institute of Technology Ibaraki College Nakane 866 Hitachinaka Ibaraki 312-8508 Japan

We present Monte Carlo data of the stress-strain diagrams obtained using two different triangulated surface models. The first is the canonical surface model of Helfrich and Polyakov (HP), and the second is a Finsler geometry (FG) model. The shape of the experimentally observed stress-strain diagram is called J-shaped. Indeed, the diagram has a plateau for the small strain region and becomes linear in the relatively large strain region. Because of this highly nonlinear behavior, the J-shaped diagram is far beyond the scope of the ordinary theory of elasticity. Therefore, the mechanism behind the J-shaped diagram still remains to be clarified, although it is commonly believed that the collagen degrees of freedom play an essential role. We find that the FG modeling technique provides a coarse-grained picture for the interaction between the collagen and the bulk material. The role of the directional degrees of freedom of collagen molecules or fibers can be understood in the context of FG modeling. We also discuss the reason for why the J-shaped diagram cannot (can) be explained by the HP (FG) model.

关键词： Anelastic deformation Elastic deformation Mechanical deformation Biological materials Elastomers metropolis algorithm

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Fracton topological order from nearest-neighbor two-spin interactions and dualities

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Physical Review B 2017年第16期96卷 165106-165106页

作者： Kevin Slagle Yong Baek Kim Department of Physics University of Toronto Toronto Ontario M5S 1A7 Canada Canadian Institute for Advanced Research Toronto Ontario M5G 1Z8 Canada

Fracton topological order describes a remarkable phase of matter, which can be characterized by fracton excitations with constrained dynamics and a ground-state degeneracy that increases exponentially with the length of the system on a three-dimensional torus. However, previous models exhibiting this order require many-spin interactions, which may be very difficult to realize in a real material or cold atom system. In this work, we present a more physically realistic model which has the so-called X-cube fracton topological order [Vijay, Haah, and Fu, Phys. Rev. B 94, 235157 (2016)] but only requires nearest-neighbor two-spin interactions. The model lives on a three-dimensional honeycomb-based lattice with one to two spin-1/2 degrees of freedom on each site and a unit cell of six sites. The model is constructed from two orthogonal stacks of Z2 topologically ordered Kitaev honeycomb layers [Kitaev, Ann. Phys.321, 2 (2006)], which are coupled together by a two-spin interaction. It is also shown that a four-spin interaction can be included to instead stabilize 3+1D Z2 topological order. We also find dual descriptions of four quantum phase transitions in our model, all of which appear to be discontinuous first-order transitions.

关键词： Quantum phase transitions Topological phases of matter Duality Kitaev model metropolis algorithm Perturbation theory

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Thermal fluctuations of the Josephson current in a ring of superconducting grains

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Physical Review B 2017年第1期95卷 014520-014520页

作者： D. A. Garanin E. M. Chudnovsky Physics Department Lehman College and Graduate School The City University of New York 250 Bedford Park Boulevard West Bronx New York 10468-1589 USA

Thermal fluctuations of the Josephson current induced by the magnetic flux through a ring of N superconducting grains are studied. When a half-fluxon is threading the ring, I exhibits incoherent transitions between the two degenerate states due to thermal phase slips. We propose a numerical method to deal with both equilibrium and dynamic properties of Josephson systems. Computed transition rate has the form Γ=A(N)exp[−B(N)/T], where B(N) agrees with the analytical result derived for the energy barrier associated with phase slips. In the nondegenerate case (e.g., at a quarter-fluxon) the equilibrium value of I decreases with T due to harmonic excitations and then gets destroyed by phase slips.

关键词： Josephson effect XY model 1-dimensional systems Tunnel junctions metropolis algorithm Molecular dynamics

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Fermion bag approach to Hamiltonian lattice field theories in continuous time

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Physical Review D 2017年第11期96卷 114502-114502页

作者： Emilie Huffman Shailesh Chandrasekharan Duke University Durham North Carolina 27708 USA

We extend the idea of fermion bags to Hamiltonian lattice field theories in the continuous time formulation. Using a class of models we argue that the temperature is a parameter that splits the fermion dynamics into small spatial regions that can be used to identify fermion bags. Using this idea we construct a continuous time quantum Monte Carlo algorithm and compute critical exponents in the 3d Ising Gross-Neveu universality class using a single flavor of massless Hamiltonian staggered fermions. We find η=0.54(6) and ν=0.88(2) using lattices up to N=2304 sites. We argue that even sizes up to N=10,000 sites should be accessible with supercomputers available today.

关键词： Lattice field theory Many-body techniques metropolis algorithm

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Finite-size analysis of the detectability limit of the stochastic block model

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Physical Review E 2017年第6期95卷 062304-062304页

作者： Jean-Gabriel Young Patrick Desrosiers Laurent Hébert-Dufresne Edward Laurence Louis J. Dubé Département de Physique de Génie Physique et d'Optique Université Laval Québec (Québec) Canada G1V 0A6 Centre de recherche de l'Institut universitaire en santé mentale de Québec Québec (Québec) Canada G1J 2G3 Santa Fe Institute Santa Fe New Mexico 87501 USA

It has been shown in recent years that the stochastic block model is sometimes undetectable in the sparse limit, i.e., that no algorithm can identify a partition correlated with the partition used to generate an instance, if the instance is sparse enough and infinitely large. In this contribution, we treat the finite case explicitly, using arguments drawn from information theory and statistics. We give a necessary condition for finite-size detectability in the general SBM. We then distinguish the concept of average detectability from the concept of instance-by-instance detectability and give explicit formulas for both definitions. Using these formulas, we prove that there exist large equivalence classes of parameters, where widely different network ensembles are equally detectable with respect to our definitions of detectability. In an extensive case study, we investigate the finite-size detectability of a simplified variant of the SBM, which encompasses a number of important models as special cases. These models include the symmetric SBM, the planted coloring model, and more exotic SBMs not previously studied. We conclude with three appendices, where we study the interplay of noise and detectability, establish a connection between our information-theoretic approach and random matrix theory, and provide proofs of some of the more technical results.

关键词： Community structure Continuous phase transition Erdos-Renyi graph Stochastic networks Uncorrelated network Block models metropolis algorithm

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Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders

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Physical Review E 2017年第2期96卷 022140-022140页

作者： Sebastian J. Wetzel Institut für Theoretische Physik Universität Heidelberg Philosophenweg 16 69120 Heidelberg Germany

We examine unsupervised machine learning techniques to learn features that best describe configurations of the two-dimensional Ising model and the three-dimensional XY model. The methods range from principal component analysis over manifold and clustering methods to artificial neural-network-based variational autoencoders. They are applied to Monte Carlo–sampled configurations and have, a priori, no knowledge about the Hamiltonian or the order parameter. We find that the most promising algorithms are principal component analysis and variational autoencoders. Their predicted latent parameters correspond to the known order parameters. The latent representations of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.

关键词： Antiferromagnetism Classical statistical mechanics Ferromagnetism Magnetic order Magnetic phase transitions Order parameters Phase transitions Artificial neural networks Classical spin models Ising model metropolis algorithm

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Atomistic simulation of finite-temperature magnetism of nanoparticles: Application to cobalt clusters on Au(111)

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Physical Review B 2017年第18期95卷 184406-184406页

作者： A. Lászlóffy L. Udvardi L. Szunyogh Department of Theoretical Physics Budapest University of Technology and Economics Budafoki út 8. HU-1111 Budapest Hungary MTA-BME Condensed Matter Research Group Budapest University of Technology and Economics Budafoki út 8. HU-1111 Budapest Hungary

We developed a technique to determine suitable spin models for small embedded clusters of arbitrary geometry by combining the spin-cluster expansion with the relativistic disordered local moment scheme. We present results for uncovered and covered hexagonal Co clusters on Au(111) surface, and use classical Monte Carlo simulations to study the temperature dependent properties of the systems. To test the new method we compare the calculated spin-model parameters of the uncovered clusters with those of a Co monolayer deposited on Au(111). In general, the isotropic and Dzyaloshinsky-Moriya interactions are larger between atoms at the perimeter than at the center of the clusters. For Co clusters covered by Au, both the contribution to the magnetic anisotropy and the easy axis direction of the perimeter atoms differ from those of the inner atoms due to reduced symmetry. We investigate the spin reversals of the covered clusters with perpendicular magnetic anisotropy and based on the variance of the magnetization component parallel to the easy direction we suggest a technique to determine the blocking temperature of superparamagnetic particles. We also determine the Néel relaxation time from the Monte Carlo simulations and find that it satisfies the Néel-Arrhenius law with an energy barrier close to the magnetic anisotropy energy of the clusters.

关键词： Exchange interaction First-principles calculations Superparamagnetism Nanoclusters Korringa-Kohn-Rostoker method metropolis algorithm Monte Carlo methods

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Complex free-energy landscapes in biaxial nematic liquid crystals and the role of repulsive interactions: A Wang-Landau study

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Physical Review E 2017年第3期96卷 032703-032703页

作者： B. Kamala Latha K. P. N. Murthy V. S. S. Sastry School of Physics University of Hyderabad Hyderabad 500046 India Centre for Modelling Simulation and Design University of Hyderabad Hyderabad 500046 India

General quadratic Hamiltonian models, describing the interaction between liquid-crystal molecules (typically with D2h symmetry), take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram (contravening in some regions of model parameter space), the predictions of mean-field theory, and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase. The free-energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes. On the one hand, these profiles account for the unusual thermal behavior of the biaxial order parameter under significant destabilizing influence from the cross terms. On the other, they also allude to the possibility that in real systems, these complexities might indeed be inhibiting the formation of a low-temperature biaxial order itself—perhaps reflecting the difficulties in their ready realization in the laboratory.

关键词： Continuous symmetries in condensed matter Entropic sampling methods Lattice models in condensed matter metropolis algorithm Monte Carlo methods

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Nuclear shape evolution based on microscopic level densities

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Physical Review C 2017年第2期95卷 024618-024618页

作者： D. E. Ward B. G. Carlsson T. Døssing P. Möller J. Randrup S. Åberg Mathematical Physics Lund University Box 118 S-221 00 Lund Sweden Niels Bohr Institute DK-2100 Copenhagen Ø Denmark Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Nuclear Science Division Lawrence Berkeley National Laboratory Berkeley California 94720 USA

By combining microscopically calculated level densities with the metropolis walk method, we develop a consistent framework for treating the energy and angular-momentum dependence of the nuclear shape evolution in the fission process. For each nucleus under consideration, the level density is calculated microscopically for each of more than five million shapes with a recently developed combinatorial method. The method employs the same single-particle levels as those used for the extraction of the pairing and shell contributions to the macroscopic-microscopic potential-energy surface. Containing no new parameters, the treatment is suitable for elucidating the energy dependence of the dynamics of warm nuclei on pairing and shell effects. It is illustrated for the fission fragment mass distribution for several uranium and plutonium isotopes of particular interest.

关键词： Energy levels & level densities Fission Nuclear charge distribution Random walks metropolis algorithm

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