Abstract
The phase transitions of Ising-type models and hard-core particle models may be related to percolation transitions of correlated percolation problems. Based on such connections, Hu has defined percolating geometrical factors G p and nonpercolating geometrical factors G f from which one may construct percolation renormalization group methods to study the lattice models. In this paper, we extend a static Monte Carlo method to calculate G p and G f. The free energies and bond fluctuations calculated from such G p and G f are very accurate when compared with exact results for finite systems. Our method is simpler than the method considered by Ferrenberg and Swendsen. Such G p and G f may be used to construct an efficient Monte Carlo renormalization group method for studying phase transitions of lattice systems.
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