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Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $σ$-Models

Gustavo Mana·Tereza Mendes·Andrea Pelissetto·Alan D. Sokal
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Abstract

We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear $σ$-models: it is based on embedding an $XY$ model into the given $σ$-model, and then updating the induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional $O(N)$ $σ$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We find that the dynamic critical exponent $z$ varies systematically between these different asymptotically free models: it is approximately 0.70 for $O(3)$, 0.60 for $O(4)$, 0.50 for $O(8)$, and 0.45 for $SU(3)$. It goes without saying that we have no theoretical explanation of this behavior.

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Gustavo Mana, Tereza Mendes, Andrea Pelissetto, Alan D. Sokal. 1995-09-12. Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $σ$-Models. https://doi.org/10.1016/0920-5632(96)00177-6

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