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A Guide to Monte Carlo Simulations in Statistical Physics by Kurt Binder, David P. Landau

By Kurt Binder, David P. Landau

Facing all points of Monte Carlo simulation of advanced actual platforms encountered in condensed-matter physics and statistical mechanics, this booklet presents an creation to machine simulations in physics. This version now includes fabric describing robust new algorithms that experience seemed because the past variation was once released, and highlights contemporary technical advances and key functions that those algorithms now make attainable. Updates additionally comprise a number of new sections and a bankruptcy at the use of Monte Carlo simulations of organic molecules. in the course of the e-book there are lots of purposes, examples, recipes, case reviews, and routines to assist the reader comprehend the fabric. it's perfect for graduate scholars and researchers, either in academia and undefined, who are looking to study recommendations that experience develop into a 3rd device of actual technology, complementing scan and analytical concept.

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Depending on the physical system, an order parameter may be measured by a variety of experimental methods such as neutron scattering, where Bragg peaks of superstructures in antiferromagnets allow the estimation of the order parameter from the integrated intensity, oscillating magnetometer measurement directly determines the spontaneous magnetization of a ferromagnet, while NMR is suitable for the measurement of local orientational order. 2 Correlation function Even if a system is not ordered, there will in general be microscopic regions in the material in which the characteristics of the material are correlated.

Thus, the loci of all points at which phase transitions occur form phase boundaries in a multidimensional space of thermodynamic fields. The classic example of a phase diagram is that of water, shown in pressure– temperature space in Fig. 1 Thermodynamics and statistical mechanics: a quick reminder 15 Fig. 3 (left) Schematic temperature dependence of the free energy and the internal energy for a system undergoing a first order transition; (right) schematic temperature dependence of the free energy and the internal energy for a system undergoing a second order transition.

Other classical models with suitable competing interactions or lattice structures may also show ‘unusual’ transitions (Landau, 1994) which in some cases include different behavior of multiple order parameters at Tc and which are generally amenable to study by computer simulation. The above discussion was confined to static aspects of phase transitions and critical phenomena. The entire question of dynamic behavior will be treated in a later section using extensions of the current formulation. 6 Universality and scaling Homogeneity arguments also provide a way of simplifying expressions which contain thermodynamic singularities.

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