The Ising model below T_c: calculation of nonuniversal amplitudes using a primitive droplet model

Abstract

Using recent exact results for the surface free energies of Ising droplets on a square lattice, and applying a primitive droplet theory due to Langer (1967), the author obtains an expression for the principal nonuniversal amplitude appearing in the imaginary part of the analytic continuation of the free energy across the coexistence line for the square lattice Ising model below Tc. The significance of this calculation is the known dependence on this amplitude of the large-order terms in the expansion of the physical free energy in powers of H, thus allowing a direct numerical comparison with existing series data to be made. After carrying out a simple renormalisation of the droplet volume term, the author finds excellent numerical agreement.