The self-consistent diagram approximation for lattice systems

G. S. Bokun; Ya. G. Groda; V. V. Belov; C. Uebing; V. S. Vikhrenko

doi:10.1007/s100510051128

EPJ

The self-consistent diagram approximation for lattice systems

G. S. Bokun¹, Ya. G. Groda¹, V. V. Belov¹, C. Uebing² and V. S. Vikhrenko¹

¹ Belarussian State Technological University 13a Sverdlova Str., Minsk 220 050, Belarus
² Max-Planck-Institut für Eisenforschung, Postfach 140 444, 40074 Düsseldorf, Germany

Received: 18 March 1999
Revised: 8 November 1999
Published online: 15 May 2000

Abstract

We apply the self-consistent diagram approximation to calculate equilibrium properties of lattice systems. The free energy of the system is represented by a diagram expansion in Mayer-like functions with averaging over states of a reference system. The latter is defined by one-particle mean potentials, which are calculated using the variational condition formulated. As an example, numerical computations for a two-dimensional lattice gas on a square lattice with attractive interaction between nearest neighbours were carried out. The critical temperature, the phase coexistence curve, the chemical potential and particle and vacancy distribution functions coincide within a few per cent with exact or with Monte Carlo data.

PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.70.Ce – Thermodynamic functions and equations of state / 64.60.-i – General studies of phase transitions