Mean field analysis of the lattice gas model in a cubic system

Abstract Ideal gases adhere to the principles of the kinetic theory of gases. To illustrate their non-ideal characteristics, we derive the equation of state for the lattice gas model defined on a cubic lattice through the application of mean field theory. This distinctive equation incorporates a logarithmic term in volume that closely resembles the Saha-Basu equation of state. We investigate the critical points and critical exponents associated with the continuous phase transition relevant to this equation. Furthermore, we compare the universal aspect of the law of corresponding states with other non-ideal equations of state. In addition, the equations related to the critical constants, including Boyle’s temperature, the Joule–Thomson coefficient, inversion temperature, and heat capacity relationships, have been derived from the equation of state. We are confident that this research will be beneficial for both undergraduate and postgraduate students specializing in statistical mechanics.