Singularity of Specific Heat in the Second Order Phase Transition

Ryuzo Abe
1967 Progress of theoretical physics  
On the basis of Fisher's method, singularity of specific heat near the transition point is studied for the Ising or Heisenberg model with an arbitrary value of spin and range of interaction. The following results are obtained for a reasonable distribution of zeros of canonical partition function. (a) If the specific heat has a singularity C,_ (T --Tc) -a above the transition point Tc, it should have a singularity C_ (Tc-T) -a below Tc, C_ being not necessarily equal to C+. (b) If the specific
more » ... at has a logarithmic singularity -A ln(T-Tc) +B+ above Tc, it should have a singularity -A ln(Tc-T) + B_ below Tc, B_ being not necessarily equal to B +· Some theoretical and experimental works so far reported are discussed in the light of these results. § I. Introduction In a previous paper 1 > (to be referred to as I), we discussed a logarithmic singularity of specific heat near the transition point in the Ising model with nearest-neighbor interaction. This paper is concerned with an extension of I to a more general physical system as well as to a more general singularity of specific heat. It is sometimes assumed that the specific heat near the transition point 1n the second order phase transition is expressed as where T is the absolute temperature, Tc the transition temperature and the suffix + or -stands for the case T>Tc or T0. In this paper, we arc going to clarify under what conditions the singularity of Eq. (1·1) can be derived, restricting ourselves to the Ising or Heisenberg model with an arbitrary value of spin and range of interaction. In § 2 following Fisher's theory, 2 > we express the canonical partition function in terms
doi:10.1143/ptp.38.322 fatcat:q6zcwsxf45csngn4ivciw3vkmu