Note on Singularity of Specific Heat in the Second Order Phase Transition

TLDR: In this paper, the singularity of specific heat near the transition point is investigated in terms of the dis-tribution of zeros of the partition function in the complex temperature plane.

Abstract: Singularity of specific heat near the transition point is investigated in terms of the dis­ tribution of. zeros of the partition function in the complex temperature plane. In the case of a centrally symmetric two-dimensional distribution of zeros, the singularity of the radial dis­ tribution function of zeros reflects directly the anomaly of specific heat. Consequently, it is shown that in general the specific heat does not necessarily take the same critical indices above and below the transition point. The modified Slater KDP model solved exactly by Wu gives a nice example to our theory. The radial distribution function of zeros in the complex z(=eC!lcT) plane for this model is given by the equation g(r) =1/(rc2rv4-=i2). Then, the sin­ gularity of the specific heat for this model takes the form C+"'(T-Tc)- 1 1 2 for T>Tc and