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Critical and multicritical behavior in the Ising-Heisenberg universality class

PHYSICS LETTERS A 2018年第48期382卷 3455-3462页

作者： Sorokin, A. O. NRC Kurchatov Inst Petersburg Nucl Phys Inst Gatchina 188300 Russia

Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit describes a single phase transition with a symmetry class differing from the class of non-frustrated magnets as well as from the classes of magnets with non-collinear spin ordering. A symmetry breaking is described by a pair of independent order parameters, which are similar to order parameters of the Ising and O(N) models correspondingly. Using the renormalization group method, it is shown that a transition is of first order for non-Ising spins. For Ising spins, a second order phase transition from the universality class of the O(2) model may be observed. The lattice models are considered by Monte Carlo simulations based on the wang-landau algorithm. The models are a ferromagnet on a body-centered cubic lattice with the additional antiferromagnetic exchange interaction between next-nearest-neighbor spins and an antiferromagnet on a simple cubic lattice with the additional interaction in layers. We consider the cases N = 1, 2, 3 and in all of them find a first-order transition. For the N = 1 case we exclude possibilities of the second order or pseudo-first order of a transition. An almost second order transition for large N is also discussed. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Frustrated magnets Phase transitions Order from disorder Monte Carlo simulations wang-landau algorithm Renormalization group

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Convergence estimation of flat-histogram algorithms based on simulation results

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COMPUTER PHYSICS COMMUNICATIONS 2018年 228卷 38-43页

作者： Shakirov, T. Univ Halle Inst Phys D-06120 Halle Germany

The present work considers the question of convergence of wang-landau, multi-canonical and stochastic approximation Monte Carlo algorithms, which was previously investigated on very different levels. In the case of the multi-canonical algorithms, a convergence behavior similar to either the original wang landau or the stochastic approximation Monte Carlo algorithms is shown, depending on details of the algorithm. I suggest a method for error estimation based only on the results of simulations, not involving an information about the exact density of states, which is unknown for most practically interesting problems. (C) 2018 Elsevier *** rights reserved.

关键词： Flat histogram Convergence wang-landau algorithm Multi-canonical Monte Carlo SAMC

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Phase diagram of a general biaxial nematic model based on density of states computation

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LIQUID CRYSTALS 2018年第13-15期45卷 2197-2213页

作者： Latha, B. Kamala Sastry, V. S. S. Univ Hyderabad Sch Phys Hyderabad Telangana India Univ Hyderabad Ctr Modelling Simulat & Design Hyderabad Telangana India

The phase diagram of a general biquadratic Hamiltonian model of biaxial nematic liquid crystals was investigated both analytically through mean-field approximation and with computer simulations. However, their largely concurrent predictions are not borne out by experimentation, and the issue is still debated. We revisited this problem with Monte Carlo simulations based on the computation of density of states of the system through entropic sampling procedure, traversing through the relevant model parameter space (S) along representative trajectories. Our recent work indicated that the competing roles of different contributions in the Hamiltonian over significant regions of S could be the underlying entropic reason defying the earlier predictions. We find that our data differ from the reported results qualitatively, specifically as the trajectories approach the so-called partly repulsive regions of S. The complex free-energy profiles that we obtain in such cases, as a function of system order parameters, indicate entropic barriers to the development of the biaxial order to the expected degree. Significant increase in the influence of the intermolecular interactions between the uniaxial and biaxial tensors, at the expense of contributions from pure biaxial couplings, is indicated to be the inhibiting factor for the onset of the biaxial phase. [GRAPHICS] .

关键词： Biaxial nematics phase diagrams density of states computation wang-landau algorithm frontier sampling free-energy curves entropic ensemble

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Structural Properties of Star-Shaped Polyions: Entropic Sampling

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POLYMER SCIENCE SERIES A 2017年第4期59卷 579-591页

作者： Silanteva, I. A. Yurchenko, A. A. Vorontsov-Velyaminov, P. N. St Petersburg State Univ Fac Phys Univ Skya Nab 7-9 St Petersburg 199034 Russia

The method of entropic sampling within the wang-landau algorithm (a modern variant of the Monte Carlo method) is used to determine the densities of energy states of a strongly charged star-shaped polyelectrolyte within the framework of the lattice model. The equilibrium thermal and structural properties of the polyelectrolyte with the number of arms f <= 6 and the length of arms N-arm <= 73 in a wide temperature range are determined from the density of states. Such characteristics as the free energy, the mean-squared radius of gyration, its components, and the parameters characterizing the shape of a polyion are calculated. It is found that the concentration, length, and number of arms affect the thermal and structural properties. The main attention is focused on the effect of temperature on these properties. The coil-to-globule transition is detected, while for the polyion with the highest length of arms (N-arm - 24) the transition from the liquid globule to the crystal-like one is observed. Differences in the properties of the star-shaped and corresponding linear polyions are characterized.

关键词： CRYSTAL structure POLYIONS ENTROPY wang-landau algorithm CRYSTAL lattices POLYELECTROLYTES

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Polymer Folding in Slitlike Nanoconfinement

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MACROMOLECULES 2017年第17期50卷 6967-6976页

作者： Taylor, Mark P. Hiram Coll Dept Phys Hiram OH 44234 USA

A flexible homopolymer chain with sufficiently short-range interactions undergoes a discontinuous transition from an expanded coil to a compact crystallite analogous to the all-or-none folding transition exhibited by fast-folding proteins. In this work we investigate the effects of both tethering and confinement on this type of folding transition. In particular, we study a flexible square-well N-mer chain (monomer diameter sigma) located between two hard walls forming a slitlike pore (width W) with the chain end tethered to one wall. We carry out Monte Carlo simulations with wang-landau sampling to construct the single-chain density of states and use both microcanonical and canonical analyses- to characterize phase transitions. We find that in a very wide pore (W > N sigma) the all-or-none folding transition is only slightly affected by the tethering. As the pore width is reduced to near the size of the folded polymer chain (W approximate to N-1/3 sigma) there is a modest entropy reduction for the unfolded states leading to a stabilization of the folded state. Below a critical slit width the chain is unable to fold into the native ground state. However, discontinuous all-or-none folding still occurs to higher energy ground-state structures commensurate with the slit width. All-or-none folding persists even to the limit of a very narrow pore (W approximate to sigma) where the ground state structure is a quasi-two-dimensional crystal. Both structural and thermodynamic effects of confinement are studied including quantitative analyses of entropy reduction and changes to the free energy barrier to folding.

关键词： POLYMERS wang-landau algorithm PHASE transformations (Physics) MONTE Carlo method ENTROPY

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A 1/t algorithm with the density of two states for estimating multidimensional integrals

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COMPUTER PHYSICS COMMUNICATIONS 2017年 220卷 122-128页

作者： Atisattapong, Wanyok Marupanthorn, Pasin Thammasat Univ Fac Sci & Technol Dept Math & Stat Pathum Thani 12120 Thailand Rajamangala Univ Technol Suvanabhumi Fac Sci & Technol Dept Math Phranakhon Si Ayutthaya 13000 Thailand

In this work we developed a 1/t algorithm for numerical integration in high dimensions. A large amount of computation time is wasted when a random walker is unable to reach a rare state at the sharp peak of an integrand, and becomes trapped after falling through that state. In this study, the density of states was divided into only two levels by sampling an arbitrary point in the range of the integrand, rather than into many levels using a fixed bin width (grid discretization on continuous space). The technique is quite straightforward and easy to implement. It avoids the need to determine the exact boundaries of the integrand, which is often a non-trivial task. Simulations show that our method is able to significantly reduce the number of Monte Carlo trials required, and therefore the simulation time. The potential of the proposed method was demonstrated by application to two multidimensional integrals: the Gaussian ring and the setting sun Feynman diagram. The results confirm that the proposed method can be applied to the calculation of multidimensional integrals without error saturation, yielding accurate values in applications where other numerical methods fail. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Monte Carlo integration wang-landau algorithm Gaussian integrals

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Degeneracy estimation in interference models on wireless networks

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2017年 469卷 540-550页

作者： McBride, Neal Bulava, John Galiotto, Carlo Marchetti, Nicola Macaluso, Irene Doyle, Linda Trinity Coll Dublin CONNECT Ctr Future Networks & Commun Dublin Ireland Trinity Coll Dublin Sch Math Dublin Ireland

We present a Monte Carlo study of interference in real-world wireless networks using the Potts model. Our approach maps the Potts energy to discrete interference levels. These levels depend on the configurations of radio frequency allocation in the network. For the first time, we estimate the degeneracy of these interference levels using the wang-landau algorithm. The cumulative distribution function of the resulting density of states is found to increase rapidly at a critical interference value. We compare these critical values for several different real-world interference networks and Potts models. Our results show that models with a greater number of available frequency channels and less dense interference networks result in the majority of configurations having lower interference levels. Consequently, their critical interference levels occur at lower values. Furthermore, the area under the density of states increases and shifts to lower interference values. Therefore, the probability of randomly sampling low interference configurations is higher under these conditions. This result can be used to consider dynamic and distributed spectrum allocation in future wireless networks. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Potts model wang-landau algorithm Degeneracy Interference modelling Distributed spectrum allocation Future wireless networks operation and design

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Self-healing umbrella sampling: convergence and efficiency

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STATISTICS AND COMPUTING 2017年第1期27卷 147-168页

作者： Fort, Gersende Jourdain, Benjamin Lelievre, Tony Stoltz, Gabriel CNRS LTCI 46 Rue Barrault F-75634 Paris 13 France Telecom Paris Tech 46 Rue Barrault F-75634 Paris 13 France Univ Paris Est CERMICS ENPC INRIA F-77455 Marne La Vallee France

The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing algorithm which has been proposed in Marsili et al. (J Phys Chem B 110(29):14011-14013, 2006) in order to efficiently sample a multimodal probability measure. We show that this method can be seen as a variant of the well-known wang-landau algorithm wang and landau (Phys Rev E 64:056101, 2001a;Phys Rev Lett 86(10):2050-2053, 2001b). Adapting results on the convergence of the wang-landau algorithm obtained in Fort et al. (Math Comput 84(295):2297-2327, 2014a), we prove the convergence of the SHUS algorithm. We also compare the two methods in terms of efficiency. We finally propose a modification of the SHUS algorithm in order to increase its efficiency, and exhibit some similarities of SHUS with the well-tempered metadynamics method Barducci et al. (Phys Rev Lett 100:020,603, 2008).

关键词： wang-landau algorithm Stochastic approximation algorithm Free energy biasing techniques

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Optimally Adjusted Mixture Sampling and LocallyWeighted HistogramAnalysis

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2017年第1期26卷 54-65页

作者： Tan, Zhiqiang Rutgers State Univ Dept Stat 110 Frelinghuysen Rd Piscataway NJ 08854 USA

Consider the two problems of simulating observations and estimating expectations and normalizing constants for multiple distributions. First, we present a self-adjusted mixture sampling method, which accommodates both adaptive serial tempering and a generalized wang-landau algorithm. The set of distributions are combined into a labeled mixture, with the mixture weights depending on the initial estimates of log normalizing constants (or free energies). Then, observations are generated by Markov transitions, and free energy estimates are adjusted online by stochastic approximation. We propose two stochastic approximation schemes by Rao-Blackwellization of the scheme commonly used, and derive the optimal choice of a gainmatrix, resulting in the minimum asymptotic variance for free energy estimation, in a simple and feasible form. Second, we develop an offline method, locally weighted histogram analysis, for estimating free energies and expectations, using all the simulated data from multiple distributions by either self-adjusted mixture sampling or other sampling algorithms. This method can be computationally much faster, with little sacrifice of statistical efficiency, than a global method currently used, especially when a large number of distributions are involved. We provide both theoretical results and numerical studies to demonstrate the advantages of the proposed methods.

关键词： Free energy Markov chain Monte Carlo Normalizing constant Parallel tempering Potts model Serial tempering Stochastic approximation wang-landau algorithm Weighted histogram analysis method

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Rupturing the hemi-fission intermediate in membrane fission under tension: Reaction coordinates, kinetic pathways, and free-energy barriers

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JOURNAL OF CHEMICAL PHYSICS 2017年第6期147卷 064906-064906页

作者： Zhang, Guojie Mueller, Marcus Univ Gottingen Inst Theoret Phys Friedrich Hund Pl 1 D-37077 Gottingen Germany

Membrane fission is a fundamental process in cells, involved inter alia in endocytosis, intracellular trafficking, and virus infection. Its underlying molecular mechanism, however, is only incompletely understood. Recently, experiments and computer simulation studies have revealed that dynamin-mediated membrane fission is a two-step process that proceeds via a metastable hemi-fission intermediate (or wormlike micelle) formed by dynamin's constriction. Importantly, this hemi-fission intermediate is remarkably metastable, i.e., its subsequent rupture that completes the fission process does not occur spontaneously but requires additional, external effects, e.g., dynamin's (unknown) conformational changes or membrane tension. Using simulations of a coarse-grained, implicit-solvent model of lipid membranes, we investigate the molecular mechanism of rupturing the hemi-fission intermediate, such as its pathway, the concomitant transition states, and barriers, as well as the role of membrane tension. The membrane tension is controlled by the chemical potential of the lipids, and the free-energy landscape as a function of two reaction coordinates is obtained by grand canonical wang-landau sampling. Our results show that, in the course of rupturing, the hemi-fission intermediate undergoes a "thinning -> local pinching -> rupture/fission" pathway, with a bottle-neck-shaped cylindrical micelle as a transition state. Although an increase of membrane tension facilitates the fission process by reducing the corresponding free-energy barrier, for biologically relevant tensions, the free-energy barriers still significantly exceed the thermal energy scale k(B)T. Published by AIP Publishing.

关键词： NUCLEAR fission METASTABLE ions LIPID membranes ACTIVATION energy wang-landau algorithm

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