A simplified method of applying a renormalization-group analysis to Monte Carlo simulations of general systems is presented and illustrated with applications to the Ising model and the three-state Potts model.
We implement a momentum-space renormalization-group procedure into the Monte Carlo renormalization-group (MCRG) method. Usually the symmetries of the system must be known and incorporated into the renormalization group, but here we let the renormalization group be given by the Monte Carlo simulation itself. This allows the MCRG method to be applicable to systems where the underlying symmetries may not be known, such as in Monte Carlo studies of quantum systems. As a test of this method, we apply it to the study of the two-dimensional square-lattice q-state Potts model, both for integer values of q and for noninteger values of q near q=4.
A Monte Carlo renormalization-group (MCRG) method developed to study quantum systems is presented. This MCRG method is the synthesis of the Monte Carlo method for quantum systems using the Trotter transformation with the MCRG developed for classical systems. It is applicable to the study of either the ground-state or the finite-temperature behavior of a quantum system. The convergence properties of this MCRG are illustrated by applying it to the ground state of the d=1 Ising model in a transverse magnetic field. Very rapid convergence to the known critical exponents is exhibited even for small lattice sizes.
The effectiveness of a Monte Carlo renormalization-group method is studied by applying it to the Baxter-Wu model (Ising spins on a triangular lattice with three-spin interactions). The calculations yield three relevant eigenvalues in good agreement with exact or conjectured results. We demonstrate that the method is capable of distinguishing between models expected to be in the same universality class, when one of them (four-state Potts) exhibits logarithmic corrections to the usual power-law singularities and the other (Baxter-Wu) does not.