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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.
The sixth edition of this highly successful textbook provides a detailed introduction to Monte Carlo simulation in statistical physics, which deals with the computer simulation of many-body systems in condensed matter physics and related fields of physics and beyond (traffic flows, stock market fluctuations, etc.). Using random numbers generated by a computer, these powerful simulation methods calculate probability distributions, making it possible to estimate the thermodynamic properties of various systems. The book describes the theoretical background of these methods, enabling newcomers to perform such simulations and to analyse their results. It features a modular structure, with two chapters providing a basic pedagogic introduction plus exercises suitable for university courses; the remaining chapters cover major recent developments in the field. This edition has been updated with two new chapters dealing with recently developed powerful special algorithms and with finite size scaling tools for the study of interfacial phenomena, which are important for nanoscience. Previous editions have been highly praised and widely used by both students and advanced researchers.
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.
Speech by Toyosaburo Taniguchi Dr. Kubo, Chairman, Distinguished Guests, and Friends, I am very happy, pleased and honored to be here this evening with so many distinguished guests, friends, and scholars from within this country and from different parts of the world. The Taniguchi Foundation wishes to extend a warm and sincere welcome to the many participants of the Ninth International Symposium on the Theory of Condensed Matter, which se ries was inaugurated eight years ago through the strenuous efforts of Dr. Ryogo Kubo, who is gracing us today with his presence. We are deeply indebted to Dr. Kubo, Dr. Suzuki, and their associates, who havE' spent an enormous amount of time and effort to make this particular symposium possible. We are convinced that the foundation should not be considered as what makes our symposium a success. The success is entirely due, I feel, to the continuous efforts of the Organizing Committee and of all those who have lent their support to this program. In this sense, your words of praise about the symposium, if any, should be directed to all of them. So far, I have met in person a total of 62 participants in this Division from 12 countries: Argentina, Belgium, Canada, Denmark, the Federal Republic of Germany, France, Ireland, Israel, Rumania, Switzerland, the United Kingdom, and the United States of America, with 133 participants from Japan. Those friends I have been privileged to make, I shall always treasure.
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.