Statistical Physics Approach to Liquid Crystals: Dynamics of Mobile Potts Model Leading to Smectic Phase, Phase Transition by Wang─Landau Method
TL;DR: It is shown that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T, and the whole remaining layers become orientationally disordered.
Abstract: We study the nature of the smectic–isotropic phase transition using a mobile 6-state Potts model. Each Potts state represents a molecular orientation. We show that with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by a mobile 6-state Potts spins, we observe the smectic phase dynamically formed when we cool the molecules from the isotropic phase to low temperatures (T). In order to elucidate the order of the transition and the low-T properties, we use the high-performance Wang–Landau flat energy-histogram technique. We show that the smectic phase goes to the liquid (isotropic) phase by melting/evaporating layer by layer starting from the film surface with increasing T. At a higher T, the whole remaining layers become orientationally disordered. The melting of each layer is characterized by a peak of the specific heat. Such a succession of partial transitions cannot be seen by the Metropolis algorithm. The successive layer meltings/evaporations at low T are found to have a first-order character by examining the energy histogram. These results are in agreement with experiments performed on some smectic liquid crystals.
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TL;DR: This article showed that the phase transition in the XY stacked triangular antiferromagnet is clearly of first-order, confirming results from latest Monte Carlo simulation and from a nonperturbative renormalization group.
Abstract: We show in this paper by using the Wang-Landau flat-histogram Monte Carlo method that the phase transition in the XY stacked triangular antiferromagnet is clearly of first-order, confirming results from latest Monte Carlo simulation and from a nonperturbative renormalization group, putting an end to a long-standing controversial issue.
19 citations
TL;DR: In this article, the second-order phase transition in the Potts model with extra invisible states was studied by using the Wang-Landau method, where the density of states difference (DOSD) was used to investigate the order of the phase transition and examine the critical value of $r$ changing the second to the first order transition.
Abstract: Phase transitions are ubiquitous phenomena, exemplified by the melting of ice and spontaneous magnetization of magnetic material. In general, a phase transition is associated with a symmetry breaking of a system; occurs due to the competition between coupling interaction and external fields such as thermal energy. If the phase transition occurs with no latent heat, the system experiences continuous transition, also known as second order phase transition. The ferromagnetic $q$-state Potts model with $r$ extra invisible states, introduced by Tamura, Tanaka, and Kawashima [Prog. Theor. Phys. 124, 381 (2010)], is studied by using the Wang-Landau method. The density of states difference (DOSD), $\ln g(E +\Delta E) - \ln g(E)$, is used to investigate the order of the phase transition and examine the critical value of $r$ changing the second to the first order transition.
6 citations
TL;DR: In this paper, the authors studied the properties of a nanodot embedded in a support by Monte Carlo simulation and showed that the ground-state configuration is a vortex around the dot central axis.
2 citations
TL;DR: In this paper, the authors examined issues concerning the occurrence of anomalies affecting the process of phase transitions in network structures, particularly in IT networks, Internet of Things and Internet of Everything.
Abstract: The paper discusses issues concerning the occurrence of anomalies affecting the process of phase transitions. The considered issue was examined from the perspective of phase transitions in network structures, particularly in IT networks, Internet of Things and Internet of Everything. The basis for the research was the Potts model in the context of IT networks. The author proposed the classification of anomalies in relation to the states of particular nodes in the network structure. Considered anomalies included homogeneous, heterogeneous, individual and cyclic disorders. The results of tests and simulations clearly showed the impact of anomalies on the phase transitions in the network structures. The obtained results can be applied in modelling the processes occurring in network structures, particularly in IT networks.
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TL;DR: In this article, exactly solved models of statistical mechanics are discussed. But they do not consider exactly solvable models in statistical mechanics, which is a special issue in the statistical mechanics of the classical two-dimensional faculty of science.
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7,761 citations
"Statistical Physics Approach to Liq..." refers background in this paper
...3), which is of second order [63,64] (see also discussions on antiferromagnetic Potts models in Reference [65])....
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...The exact transition temperature is given by [63]...
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TL;DR: In this paper, it is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic.
Abstract: It is rigorously proved that at any nonzero temperature, a one- or two-dimensional isotropic spin-$S$ Heisenberg model with finite-range exchange interaction can be neither ferromagnetic nor antiferromagnetic. The method of proof is capable of excluding a variety of types of ordering in one and two dimensions.
6,236 citations
Additional excerpts
...The absence of a long-range order is rigorously shown for continuous spin models such as the Heisenberg model with short-range interactions in 2D [62]....
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TL;DR: A new Monte Carlo algorithm is presented that permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions.
Abstract: We present a new Monte Carlo algorithm that produces results of high accuracy with reduced simulational effort. Independent random walks are performed (concurrently or serially) in different, restricted ranges of energy, and the resultant density of states is modified continuously to produce locally flat histograms. This method permits us to directly access the free energy and entropy, is independent of temperature, and is efficient for the study of both 1st order and 2nd order phase transitions. It should also be useful for the study of complex systems with a rough energy landscape.
2,639 citations
10 May 2011
TL;DR: A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data and its applications in environmental epidemiology, educational research, and fisheries science are studied.
Abstract: Foreword Stephen P. Brooks, Andrew Gelman, Galin L. Jones, and Xiao-Li Meng Introduction to MCMC, Charles J. Geyer A short history of Markov chain Monte Carlo: Subjective recollections from in-complete data, Christian Robert and George Casella Reversible jump Markov chain Monte Carlo, Yanan Fan and Scott A. Sisson Optimal proposal distributions and adaptive MCMC, Jeffrey S. Rosenthal MCMC using Hamiltonian dynamics, Radford M. Neal Inference and Monitoring Convergence, Andrew Gelman and Kenneth Shirley Implementing MCMC: Estimating with confidence, James M. Flegal and Galin L. Jones Perfection within reach: Exact MCMC sampling, Radu V. Craiu and Xiao-Li Meng Spatial point processes, Mark Huber The data augmentation algorithm: Theory and methodology, James P. Hobert Importance sampling, simulated tempering and umbrella sampling, Charles J.Geyer Likelihood-free Markov chain Monte Carlo, Scott A. Sisson and Yanan Fan MCMC in the analysis of genetic data on related individuals, Elizabeth Thompson A Markov chain Monte Carlo based analysis of a multilevel model for functional MRI data, Brian Caffo, DuBois Bowman, Lynn Eberly, and Susan Spear Bassett Partially collapsed Gibbs sampling & path-adaptive Metropolis-Hastings in high-energy astrophysics, David van Dyk and Taeyoung Park Posterior exploration for computationally intensive forward models, Dave Higdon, C. Shane Reese, J. David Moulton, Jasper A. Vrugt and Colin Fox Statistical ecology, Ruth King Gaussian random field models for spatial data, Murali Haran Modeling preference changes via a hidden Markov item response theory model, Jong Hee Park Parallel Bayesian MCMC imputation for multiple distributed lag models: A case study in environmental epidemiology, Brian Caffo, Roger Peng, Francesca Dominici, Thomas A. Louis, and Scott Zeger MCMC for state space models, Paul Fearnhead MCMC in educational research, Roy Levy, Robert J. Mislevy, and John T. Behrens Applications of MCMC in fisheries science, Russell B. Millar Model comparison and simulation for hierarchical models: analyzing rural-urban migration in Thailand, Filiz Garip and Bruce Western
2,415 citations
"Statistical Physics Approach to Liq..." refers methods in this paper
...To see the dynamics of the molecules upon slow cooling, we use the Metropolis algorithm [48,49]: we generate the positions and the orientations of the molecules randomly in the recipient, we update each...
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01 Jan 2014
TL;DR: In this paper, the authors describe the story of the recent developments and the future perspectives in physics of liquid crystals, especially focusing on the contributions by Japanese research groups for the last decade, and present new subjects unmentioned in the book.
Abstract: Over the 100 years since its discovery, liquid crystals have been the intriguing subject for both academia and industries. The textbook of de Gennes The Physics of Liquid Crystals published in 1974 is still the bible for many LC researchers, but new subjects unmentioned in the book have also risen for these years. This chapter describes the story of the recent developments and the future perspectives in physics of liquid crystals, especially focusing on the contributions by Japanese research groups for the last decade.
2,005 citations