High Resolution Monte Carlo Study Of Finite Size Behavior At Phase Transitions In Spin Models
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High Resolution Monte Carlo Study Of Finite Size Behavior At Phase Transitions In Spin Models
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Author : Jiahao Xu
language : en
Publisher:
Release Date : 2019
High Resolution Monte Carlo Study Of Finite Size Behavior At Phase Transitions In Spin Models written by Jiahao Xu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
We have studied the finite-size behavior at magnetic phase transitions by using extensive Monte Carlo simulations. For the second-order transition in the simple cubic Ising model, we have investigated the critical behavior by implementing the Wolff cluster flipping algorithm and data analysis with histogram reweighting in quadruple precision arithmetic. By analyzing data with cross correlations between various thermodynamic quantities obtained from the same data pool, we have obtained the critical quantities with precision that exceeds all previous Monte Carlo estimates. For the first-order ``spin-flop" transition in the 3D anisotropic Heisenberg antiferromagnet in an external field, we have explored the finite-size behavior of the transition between the Ising-like antiferromagnetic state and the canted, $XY$-like state. Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological ``degeneracy" factor, $q$, included. Our theory yields $q = pi$, and it predicts that for large linear dimension $L$ the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections, where the values of these intersections can be expressed in terms of the factor $q$. The agreement between our theory and high-resolution multicanonical simulation data implies a heretofore unknown universality can be invoked for first-order phase transitions.
Monte Carlo Simulation In Statistical Physics
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Author : Kurt Binder
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Monte Carlo Simulation In Statistical Physics written by Kurt Binder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
Dealing with the computer simulation of thermodynamic properties of many-body condensed-matter systems that use random numbers generated by a computer, this book describes the theoretical background of several variants of Monte Carlo methods. The result is a systematic course allowing newcomers to perform these simulations for themselves and to analyze their results. This third edition has been updated and expanded by a new chapter on important recent developments in the Monte Carlo methodology.
A Guide To Monte Carlo Simulations In Statistical Physics
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Author : David P. Landau
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-10
A Guide To Monte Carlo Simulations In Statistical Physics written by David P. Landau and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-10 with Science categories.
Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This edition now contains material describing powerful new algorithms that have appeared since the previous edition was published, and highlights recent technical advances and key applications that these algorithms now make possible. Updates also include several new sections and a chapter on the use of Monte Carlo simulations of biological molecules. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory.
A Guide To Monte Carlo Simulations In Statistical Physics
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Author : David P. Landau
language : en
Publisher: Cambridge University Press
Release Date : 2000-08-17
A Guide To Monte Carlo Simulations In Statistical Physics written by David P. Landau and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08-17 with Mathematics categories.
This book describes all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, as well as in related fields, such as polymer science and lattice gauge theory. The authors give a succinct overview of simple sampling methods and develop the importance sampling method. In addition they introduce quantum Monte Carlo methods, aspects of simulations of growth phenomena and other systems far from equilibrium, and the Monte Carlo Renormalization Group approach to critical phenomena. The book includes many applications, examples, and current references, and exercises to help the reader.
Monte Carlo Methods In Statistical Physics
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Author : M. E. J. Newman
language : en
Publisher: Clarendon Press
Release Date : 1999-02-11
Monte Carlo Methods In Statistical Physics written by M. E. J. Newman and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-02-11 with Science categories.
This book provides an introduction to Monte Carlo simulations in classical statistical physics and is aimed both at students beginning work in the field and at more experienced researchers who wish to learn more about Monte Carlo methods. The material covered includes methods for both equilibrium and out of equilibrium systems, and common algorithms like the Metropolis and heat-bath algorithms are discussed in detail, as well as more sophisticated ones such as continuous time Monte Carlo, cluster algorithms, multigrid methods, entropic sampling and simulated tempering. Data analysis techniques are also explained starting with straightforward measurement and error-estimation techniques and progressing to topics such as the single and multiple histogram methods and finite size scaling. The last few chapters of the book are devoted to implementation issues, including discussions of such topics as lattice representations, efficient implementation of data structures, multispin coding, parallelization of Monte Carlo algorithms, and random number generation. At the end of the book the authors give a number of example programmes demonstrating the applications of these techniques to a variety of well-known models.
Monte Carlo Simulation In Some Continuous Lattice Spin Models
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Author : Suman Sinha
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2010-11
Monte Carlo Simulation In Some Continuous Lattice Spin Models written by Suman Sinha and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11 with categories.
Using Monte Carlo simulation we have investigated a classical two-dimensional XY-model with a modified form of interaction which makes the potential well sharper than that in the conventional XY-model. The conventional XY-model is known to exhibit a defect-mediated continuous phase transition while the modified XY-model has a strong first order phase transition, both transitions being temperature driven. Performance and relative assessment of Wang-Landau (WL) algorithm in these class of models have been discussed. Difficulties faced in simulating relatively large continuous systems using WL algorithm have been investigated. Besides applying the cluster algorithm of Wolff, we have used Ferrenberg-Swendsen multiple histogram reweighting technique and finite size scaling rules of Lee and Kosterlitz. We have also investigated the role played by the topological defects and the factors which are responsible for the change over the nature of the phase transition from a continuous one to a strongly first order one. We have also presented a detailed study of the effect of suppression of topological defects on various physical quantities relevant to this model.
The Monte Carlo Method In Condensed Matter Physics
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Author : Kurt Binder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Monte Carlo Method In Condensed Matter Physics written by Kurt Binder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The Monte Carlo method is now widely used and commonly accepted as an important and useful tool in solid state physics and related fields. It is broadly recognized that the technique of "computer simulation" is complementary to both analytical theory and experiment, and can significantly contribute to ad vancing the understanding of various scientific problems. Widespread applications of the Monte Carlo method to various fields of the statistical mechanics of condensed matter physics have already been reviewed in two previously published books, namely Monte Carlo Methods in Statistical Physics (Topics Curro Phys. , Vol. 7, 1st edn. 1979, 2ndedn. 1986) and Applications of the Monte Carlo Method in Statistical Physics (Topics Curro Phys. , Vol. 36, 1st edn. 1984, 2nd edn. 1987). Meanwhile the field has continued its rapid growth and expansion, and applications to new fields have appeared that were not treated at all in the above two books (e. g. studies of irreversible growth phenomena, cellular automata, interfaces, and quantum problems on lattices). Also, new methodic aspects have emerged, such as aspects of efficient use of vector com puters or parallel computers, more efficient analysis of simulated systems con figurations, and methods to reduce critical slowing down at i>hase transitions. Taken together with the extensive activity in certain traditional areas of research (simulation of classical and quantum fluids, of macromolecular materials, of spin glasses and quadrupolar glasses, etc.
Applications Of The Monte Carlo Method In Statistical Physics
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Author : Kurt Binder
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Applications Of The Monte Carlo Method In Statistical Physics written by Kurt Binder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
Deals with the computer simulation of complex physical sys- tems encounteredin condensed-matter physics and statistical mechanics as well as in related fields such as metallurgy, polymer research, lattice gauge theory and quantummechanics.
Monte Carlo Studies Of Disordered Spin Systems
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Author : Derek A. Larson
language : en
Publisher:
Release Date : 2009
Monte Carlo Studies Of Disordered Spin Systems written by Derek A. Larson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Monte Carlo Methods In Statistical Physics
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Author : Kurt Binder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Monte Carlo Methods In Statistical Physics written by Kurt Binder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In the seven years since this volume first appeared. there has been an enormous expansion of the range of problems to which Monte Carlo computer simulation methods have been applied. This fact has already led to the addition of a companion volume ("Applications of the Monte Carlo Method in Statistical Physics", Topics in Current Physics. Vol . 36), edited in 1984, to this book. But the field continues to develop further; rapid progress is being made with respect to the implementation of Monte Carlo algorithms, the construction of special-purpose computers dedicated to exe cute Monte Carlo programs, and new methods to analyze the "data" generated by these programs. Brief descriptions of these and other developments, together with numerous addi tional references, are included in a new chapter , "Recent Trends in Monte Carlo Simulations" , which has been written for this second edition. Typographical correc tions have been made and fuller references given where appropriate, but otherwise the layout and contents of the other chapters are left unchanged. Thus this book, together with its companion volume mentioned above, gives a fairly complete and up to-date review of the field. It is hoped that the reduced price of this paperback edition will make it accessible to a wide range of scientists and students in the fields to which it is relevant: theoretical phYSics and physical chemistry , con densed-matter physics and materials science, computational physics and applied mathematics, etc.
