Computer Studies of Phase Transitions and Critical Phenomena [Paperback]

1. Introduction.- 2. Computer Methods in the Study of Phase Transitions and Critical Phenomena.- 2.1 Statistical Mechanics and Phase Transitions.- 2.1.1 Modern theories of phase transitions and critical phenomena.- 2.1.2 Statistical mechanics, order parameters, fluctuations, critical exponents, scaling, and universality.- 2.2 Numerical Simulation Techniques.- 2.2.1 Monte Carlo methods.- 2.2.2 A Monte Carlo importance-sampling method.- 2.2.3 A realization of a Monte Carlo method.- 2.2.4 General limitations of the Monte Carlo method.- 2.2.5 Broken ergodicity.- 2.2.6 Distribution functions.- 2.2.7 Coarse-graining techniques and criteria of convergence.- 2.2.8 Finite-size effects.- 2.2.9 Determining the nature of a phase transition.- 2.2.10 Computational details.- 2.2.11 General advantages of the Monte Carlo method: Applications.- 2.3 Exact Configurational Counting and Series Expansions.- 2.3.1 A general approach.- 2.3.2 The moment method.- 2.3.3 Principles of the calculation.- 2.3.4 Step 1. Determination of all distinct graphs and their multiplicities.- 2.3.5 Step 2. Embedding of connected graphs into a lattice.- 2.3.6 General correlation function series.- 2.3.7 Capabilities and limitations of a general approach.- 3. Monte Carlo Pure-model Calculations.- 3.1 Critical Behavior of the Three-dimensional Ising Model.- 3.1.1 The Ising model and its order parameter.- 3.1.2 Numerical evidence of a phase transition in the Ising model on a diamond lattice.- 3.1.3 Finite-size scaling analysis and critical behavior.- 3.1.4 Are Monte Carlo techniques practicable in the study of critical phenomena?.- 3.2 Phase Behavior of Ising Models with Multi-spin Interactions.- 3.2.1 Higher-order exchange in magnetic systems.- 3.2.2 Ising models with multi-spin interactions.- 3.2.3 First-order phase transitions of Ising models with pure multi-spin interactions.- 3.2.4 Universality and tricritical behavior of Ising models with two- and four-spin interactions: Pair interactions as a symmetry-brealc¶