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Prog. Theor. Phys. Vol. 38 No. 6 (1967) pp. 1243-1251

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

Masuo Suzuki

Department of Physics, Faculty of Science, University of Tokyo, Tokyo

(Received August 21, 1967)

Abstract:

Singularity of specific heat near the transition point is investigated in terms of the distribution 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 distribution 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 ( = e^ε/kT) plane for this model is given by the equation g(r) = 1/(π²r √4 - r²). Then, the singularity of the specific heat for this model takes the form C⁺ ∼ (T - T_c)^-1/2 for T > T_c and C^- = 0 for T < T_c.

URL : http://ptp.ipap.jp/link?PTP/38/1243/
DOI : 10.1143/PTP.38.1243

[ Full Text PDF : FREE ACCESS (412K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. T. D. Lee and C. N. Yang, Phys. Rev. 87 (1952), 410[APS].
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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 38 No. 6 (1967) pp. 1225-1242 :

   A Theory of the Second Order Phase Transitions in Spin Systems. II

   Masuo Suzuki

2. Progress of Theoretical Physics Vol. 40 No. 6 (1968) pp. 1246-1256 :

   Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism

   Masuo Suzuki

3. Progress of Theoretical Physics Vol. 41 No. 6 (1969) pp. 1438-1449 :

   On the Distribution of Zeros for the Heisenberg Model

   Masuo Suzuki

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