TY - JOUR
T1 - Multigrid Monte Carlo method. Conceptual foundations
AU - Goodman, Jonathan
AU - Sokal, Alan D.
PY - 1989
Y1 - 1989
N2 - 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 a4 model, numerical experiments show a factor of 10 reduction, over a standard heat-bath algorithm, in the CPU time needed to achieve a given accuracy. For the two-dimensional XY model, experiments show a factor of 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 models, and to lattice gauge theories with or without bosonic matter fields.
AB - 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 a4 model, numerical experiments show a factor of 10 reduction, over a standard heat-bath algorithm, in the CPU time needed to achieve a given accuracy. For the two-dimensional XY model, experiments show a factor of 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 models, and to lattice gauge theories with or without bosonic matter fields.
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U2 - 10.1103/PhysRevD.40.2035
DO - 10.1103/PhysRevD.40.2035
M3 - Article
AN - SCOPUS:3843097430
VL - 40
SP - 2035
EP - 2071
JO - Physical review D: Particles and fields
JF - Physical review D: Particles and fields
SN - 1550-7998
IS - 6
ER -