Monte Carlo Simulations of Disordered Systems
This book covers the techniques of computer simulations of disordered systems. It describes how one performs Monte Carlo simulations in condensed matter physics and deals with spin-glasses, percolating networks and the random field Ising model. Other methods mentioned are molecular dynamics and Brownian dynamics. Use of flow-diagrams enables the reader to grasp both the problem and its solution more readily. The book deals with highly complicated problems at a relatively simple level and will be most useful for advanced undergraduate and other courses in computational modelling.
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DISORDERED MODEL SYSTEMS
analytic antiferromagnetic assumed behaviour bond percolation canonical ensemble Chapter computer experiments configurations consequence consider course critical exponents critical point defined dimensionality discussed disorder distribution energy per spin equation equilibrium error evaluate example expectation value experimental ferromagnetic Figure finite fluctuations follows fractal Gaussian Gibbs free energy given Hamiltonian heat bath Hence integration interactions Ising model Ising spins known law of thermodynamics magnetization mean field theory mentioned microscopic model model system Monte Carlo estimate Monte Carlo method Monte Carlo simulations Monte Carlo technique non-zero Note obtained one-dimensional order parameter particles partition function percolation threshold phase space phase transition physical system probability density function problem quadrature rules quantities quantum mechanical random numbers random variable reader right hand side sample shown in Fig simple SiSj site-diluted solution specific heat square lattice statistical mechanics substituted summation temperature theoretician transition probability two-dimensional Ising model variance W(Si zero-field