Invaded cluster algorithm for Potts models
J. Machta, Y. S. Choi, A. Lucke, T. Schweizer (U. of Mass.), L. M., Chayes (UCLA)
TL;DR
The invaded cluster algorithm offers an efficient simulation method for phase transitions in Potts models, capable of distinguishing between first-order and continuous transitions without critical slowing.
Contribution
It introduces a new invaded cluster algorithm with theoretical justification and demonstrates its effectiveness for Potts models in multiple dimensions.
Findings
Effective in distinguishing transition types
No critical slowing observed in Ising models
Applicable to both first-order and continuous transitions
Abstract
The invaded cluster algorithm, a new method for simulating phase transitions, is described in detail. Theoretical, albeit nonrigorous, justification of the method is presented and the algorithm is applied to Potts models in two and three dimensions. The algorithm is shown to be useful for both first-order and continuous transitions and evidently provides an efficient way to distinguish between these possibilities. The dynamic properties of the invaded cluster algorithm are studied. Numerical evidence suggests that the algorithm has no critical slowing for Ising models.
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