Study of Many-State Classical Spin Systems by the Renormalization Group, Duality and Monte Carlo Simulation

C. Y. Pan

O. Elgarraoui, Hasnae Saadi, Mohamed Monkade +2 more

Hidetoshi Nishimori

A class of classical spin systems in two dimensions with symmetry of a cyclic group is studied in three ways: by the real space renormalization group technique, by the duality transformation and by a numerical experiment.The former two methods are shown to be in a close relation to each other.Useful information is obtained on the shape of the critical surface, on the behavior near the criticality and on thermodynamic quantities such as the internal energy and the magnetic susceptibility.Some of these results are compared with expected properties of the planar model, to which the present model reduces if an appropriate limit is taken.

E. Peter Münger, M. A. Novotny

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.

泰啓 日永田

M. A. Novotny, David Paul Landau

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.