Logarithmic Singularity of Specific Heat near the Transition Point in the Ising Model

Abstract

Logarithmic singularity of specific heat near the transition point is studied in the case of the Ising model with ferromagnetic nearest neighbor interaction. The parameter appearing in high temperature expansion is extended to the whole complex plane and the analytical behavior of thermodynamic functions is examined. A distribution of roots which are derived from a certain algebraic equation plays an important role of determining the singularity of specific heat. A strikingly simple distribution of roots is shown to lead to the singularity consistent with experiment. Comparison of the theory with experiment on the liquid-gas transition at the critical point is discussed.