The effective‐site percolation approach in two dimensions

Abstract

A new Monte Carlo cluster approach to describe the order -order and order -disorder transitions in twodimensional (2D) correlated systems is presented. It is shown that a phase transition of a physical system can be correctly described in terms of the percolation language of the effective-site approach. In contrast to the well-known bond approaches, the method proposed does not require additional assumptions as to the acceptance of the bonds. The new idea is based on the site approach to elementary ordered plaquettes, leading to the accurate coincidence of percolation and the phase transitions in 2D. Here I present the analysis of the spin-system in the Blume -Capel model and the charged-system in the atomic limit of the extended Hubbard model. In both cases the interpretation of the phase transition is made in terms of the percolation of different types of order. The new method allows precise identification of the pure and mixed phases.