Monte Carlo renormalization-group (MCRG) methods are described and illustrated for models of current interest. The calculation of critical exponents and the determination of critical temperatures are discussed, as well as the application to multicritical points.
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.
We introduce a computationally stable inverse Monte Carlo renormalization group transformation method that provides a number of advantages for the calculation of critical properties. We are able to simulate the fixed point of a renormalization group for arbitrarily large lattices without critical slowing down. The log-log scaling plots obtained with this method show remarkable linearity, leading to accurate estimates for critical exponents. We illustrate this method with calculations in two- and three-dimensional Ising models for a variety of renormalization group transformations.