Abstract
The Monte Carlo renormalization group (MCRG) methods and the underlying theory is 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. The problem of deteriorating exponents with long-range transformations is highlighted. Lastly, some of the existing methods for calculating the renormalized Hamiltonian are reviewed and evaluated.
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