A Guide to Monte Carlo Simulations in Statistical Physics

By David P Landau, Kurt Binder. 2000

1,229 citations recorded by the source corpus.

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. The 5th edition contains extensive new material describing numerous powerful algorithms and methods that represent recent developments in the field. New topics such as active matter and machine learning are also introduced. Throughout, there are many applications, examples, recipes, case studies, and exercises to help the reader fully comprehend the material. This book 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.

Subfields: Organic Chemistry, Physical and Theoretical Chemistry, Probabilistic & Bayesian Methods

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Citations in the corpus

A-NICE-MC: Adversarial Training for MCMC (2017, background): “This form is very common in Bayesian statistics [22], computational physics [23] and graphics [24].”
Perspectives of quantum annealing: methods and implementations (2019, methodology): “† A stoquastic Hamiltonian can generally be simulated efficiently on a classical computer by the standard method of Trotter decomposition (see [149, 150] for exceptions), which leads to non-negative effective local Boltzmann factors [151].”
Building a Telescope to Look Into High-Dimensional Image Spaces (2018, methodology): “The system will stay in a stable, predominantly negative state for a long period of time, even though the global minimum of the energy landscape is σ, because the magnetic field force cannot overcome the barriers between σ and σ− in the raw Ising energy landscape [27].”
Stochastic collocation and mixed finite elements for flow in porous media (2008, methodology): “Stochastic modeling methods can be classified in three major groups: (1) sampling methods [13,22], (2) moment/ perturbation methods [19,24,43,17,18] and, (3) non-perturbative methods, either based on polynomial chaos expansions [15,14,40–42,16] or stochastic finite element methods [15,12,3].”
An overview of spatial microscopic and accelerated kinetic Monte Carlo methods (2007, background): “, surfaces, defects, and nanoparticles), and in gas phases to study transport, thermophysical, magnetic, reactivity, andmechanical properties [2–11] is common in physics, chemistry,materials science, and engineering disciplines.”
Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, neutral): “approach is an advanced art [55], far beyond the scope (or purpose) of this review.”
Lattice Boltzmann Simulations of Soft Matter Systems (2008, methodology): “A purely microscopic approach was taken, in which the stochastic collisions werevi wed as a Monte Carlo [116] process.”
GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model (2009, methodology): “The simple Ising model, which is one of the simplest lattice models, consists of an arrangement of spins with are located on the sites of the lattice and which exhibit only the values +1 and 1 [30].”
Evolutionary dynamics of group interactions on structured populations: a review (2013, methodology): “Here, methods of statistical physics, in particular that of Monte Carlo simulations [58,73,74], are invaluable for a correct treatment.”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “A number of books have been written on the Monte Carlo method and its applications (especially in finance) [111, 112, 130, 152, 191, 213, 274, 290, 350, 354, 383], stochastic simulation [42, 159, 196, 197, 221], and quasi-Monte Carlo methods [120, 285, 313, 398].”
Machine learning quantum phases of matter beyond the fermion sign problem (2016, methodology): “approaches a common procedure [13] consists of two steps: (1) taking the absolute value of the configuration weight, thereby allowing interpretation as a probability amenable to sampling; and (2) precisely compensating for this by weighing observables (such as two-point correlation functions) with t”
The Markov chain Monte Carlo revolution (2008, neutral): “For physics, [57] and [72]. For chemistry, [41] and [ 58 ].”