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.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Nuclear and High Energy Physics