FINITE-SIZE EFFECTS IN THE APPROXIMATING HAMILTONIAN METHOD

The Husimi-Temperley mean spherical model, in which each two particles interact with equal strength, is considered. This model is shown to be equivalent to a d-dimensional model with periodic boundary conditions and interaction potential σJσ(r), where Jσ(r) ∼ r-d-σ as r→∞, σ > 0 being a parameter, in the limit σ→0. It is found that the approximating Hamiltonian method yields singular finite-size scaling functions both in the neighbourhood of the critical point and near a first-order phase transition. A modification of this method is suggested, which allows for all the essential configurations and reproduces the exact finite-size scaling near a first-order phase transition. © 1990.