Lattice field theory as a percolation process

Physical Review LettersPublished 11 April 1988

Ulli Wolff

DOI10.1103/physrevlett.60.1461

Source URL

Citations125

SJR quartileQ1

SJR score2.86

SNIP2.41

TL;DR

A new representation of lattice spin or gauge theory is conjectured to reproduce the universal scaling behavior of the original model, which lends itself to the design of Monte Carlo algorithms with reduced critical slowing down.

Abstract

For a given lattice spin or gauge theory an associated correlated bond or plaquette percolation process is constructed. It is conjectured to reproduce the universal scaling behavior of the original model. Different field theories lead to different cluster weights generalizing a result by Fortuin and Kasteleyn for Potts models. The new representation lends itself to the design of Monte Carlo algorithms with reduced critical slowing down.

Keywords

MathematicsPhysics and Astronomy

Physical Review LettersNonuniversal critical dynamics in Monte Carlo simulations

2,867 Citations1987Robert H. Swendsen, Jian‐Sheng Wang

A new approach to Monte Carlo simulations is presented, giving a highly efficient method of simulation for large systems near criticality, despite the fact that the algorithm violates dynamic universality at second-order phase transitions.

Physics ReportsScaling theory of percolation clusters

2,346 Citations1979D. Stauffer

Physical review. B, Solid statePercolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm

1,917 Citations1976Joseph Hoshen, R. Kopelman

PhysicaOn the random-cluster model

1,772 Citations1972C.M. Fortuin, Piet Kasteleyn

It is shown that the function which for the random-cluster model plays the role of a partition function, is a generalization of the dichromatic polynomial earlier introduced by Tutte, and related polynomials.

Reports on Progress in PhysicsPercolation theory

994 Citations1980J W Essam

Physical Review LettersMicrocanonical Monte Carlo Simulation

570 Citations1983Michael Creutz

A new algorithm for the simulation of statistical systems that produces a random walk through configurations of a constant total energy and is applicable to systems of both discrete and continuous variables.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsLangevin simulations of lattice field theories

384 Citations1985G. G. Batrouni, G. R. Katz +4 more

Fourier techniques that greatly accelerate simulations on large lattices and a new technique for including quark vacuum-polarization corrections that admits any number of flavors, odd or even, without the need for nested Monte Carlo calculations are introduced.

Physical Review LettersMultigrid Monte Carlo Method for Lattice Field Theories

152 Citations1986Jonathan Goodman, Alan D. Sokal

A stochastic generalization of the multigrid method, which reduces critical slowing down in Monte Carlo computations of lattice field theories, is proposed, which shows a factor of roughly-equal10 reduction in the work needed to get a given accuracy (error-bar size).

Physical review. B, Condensed matterMonte Carlo study of weighted percolation clusters relevant to the Potts models

129 Citations1983M. Sweeny

Physics Letters BPerturbation theory and zero modes in O(N) lattice σ models

68 Citations1984P. Hasenfratz

View PDF