Multigrid Monte Carlo method. Conceptual foundations

Journal Article · Fri Sep 15 04:00:00 EDT 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.2035· OSTI ID:5591952

Goodman, J ^[1]; Sokal, A D ^[2]

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1. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012 (US)
2. Department of Physics, New York University, 4 Washington Place, New York, New York 10003

We present details of a stochastic generalization of the multigrid method, called multigrid Monte Carlo (MGMC), that reduces critical slowing down in Monte Carlo computations of lattice field theories. For Gaussian (free) fields, critical slowing down is completely eliminated. For a {phi}{sup 4} model, numerical experiments show a factor of {approx}10 reduction, over a standard heat-bath algorithm, in the CPU time needed to achieve a given accuracy. For the two-dimensional {ital XY} model, experiments show a factor of {approx}10 reduction on the high-temperature side of criticality, growing to an unbounded reduction in the low-temperature regime. The algorithm is also applicable to nonlinear {sigma} models, and to lattice gauge theories with or without bosonic matter fields.

• OSTI ID: 5591952
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Journal Name: Physical Review (Section) D: Particles and Fields; (USA) Vol. 40:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGORITHMS
BOSONS
FIELD THEORIES
GAUSSIAN PROCESSES
LATTICE FIELD THEORY
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MONTE CARLO METHOD
PARTICLE MODELS
PHI4-FIELD THEORY
PROBABILITY
QUANTUM FIELD THEORY
RENORMALIZATION
SIGMA MODEL