The Monte Carlo Renormalization Group (MCRG) methods and the theory behind them are reviewed. The Gupta-Cordery improved MCRG method is described and compared with the standard one. The emphasis is on the progress made in understanding the truncation errors in the Linearized Transformation Matrix and on open problems. Lastly, some of the existing methods for calculating the renormalized Hamiltonian are reviewed and evaluated. 35 refs.

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Critical behavior of the three-state Potts model: Monte Carlo renormalization group

Robert H. Swendsen, A. Nihat Berker

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Physics Letters A

Monte Carlo renormalized hamiltonian

Rajan Gupta, Robert Cordery

Published Nov 1, 1984• 37 citations

Publisher

DOI: 10.1016/0375-9601(84)90719-9

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The

d=3

planar model is analyzed for the first time with the Monte Carlo renormalization-group (MCRG) method. To increase the efficiency of the calculation, an operator is introduced in analogy with the "vacancy" operator used in the MCRG analysis of the

q=4

Potts model. This operator is shown to be important in understanding the effect of the renormalization transformation on the Hamiltonian, and in improving the convergence of the method.