TY - JOUR
T1 - Multi-grid Monte Carlo (II). Two-dimensional XY model
AU - Edwards, Robert G.
AU - Goodman, Jonathan
AU - Sokal, Alan D.
N1 - Funding Information:
The computations reported here were carried out primarily on the VAX 860() and 8650 and Elxsi 6400 at New York University . Some computations were performed on the Cyber 205 at the John Von Neumann Supercomputer Center (JVNC). This work was supported in part by the US National Science Foundation grants PHY-8413569, PHY-8715995, DMS-8705599 and DMS-8911273, by the US Department of Energy through contract DE-FC05-85ER250000, and by JVNC grant NAC-705. One of the authors (J.G.) was partially supported by a Sloan Foundation Fellowship and by DARPA.
PY - 1991/5/6
Y1 - 1991/5/6
N2 - 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.
AB - 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.
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U2 - 10.1016/0550-3213(91)90357-4
DO - 10.1016/0550-3213(91)90357-4
M3 - Article
AN - SCOPUS:0000801777
SN - 0550-3213
VL - 354
SP - 289
EP - 327
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
IS - 2-3
ER -