Statistical Mechanics of a System of Ising Spins near the Transition Point

A linked cluster expansion for a system of Ising spins is rearranged into a form suitable for studying the phase transition of the system. A function I(q) analogous to proper self-energy part in quantum theory is introduced and shown to play an important role to determine both the transition temperature and the singularity of thermodynamic functions at the transition point. The case above the transition temperature and without magnetic field is considered, and it is proved that diagrams for I(q) dominant near the transition point have precisely the same structure as in the system of Bose fluid. Thus the method developed by Patashinsky and Pokrovsky for the latter case is taken over to the present problem and leads to a logarithmic singularity of specific heat.