Multi-grid Monte Carlo (II). Two-dimensional XY model

Robert G. Edwards, Jonathan Goodman, Alan D. Sokal

Research output: Contribution to journalArticlepeer-review


We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm applied to the two-dimensional XY model, on lattices up to 128 × 128. In the low-temperature (spin-wave) phase, we find that critical slowing-down is completely eliminated (z = 0). On the high-temperature side of critically, we find that the dynamic critical exponent is z = 1.4±0.3, compared to z = 2.1±0.3 for the heat-bath algorithm. We attribute the remaining critical slowing-down on the high-temperature side of criticality to the limited effectiveness of the MGMC updates in creating and destroying widely separated vortex-antivortex pairs.

Original languageEnglish (US)
Pages (from-to)289-327
Number of pages39
JournalNuclear Physics, Section B
Issue number2-3
StatePublished - May 6 1991

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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