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Prog. Theor. Phys. Vol. 38 No. 2 (1967) pp. 322-331

[ Full Text PDF : FREE ACCESS (596K) ]

Singularity of Specific Heat in the Second Order Phase Transition

Ryuzo Abe

Department of Pure and Applied Science, College of General Education, University of Tokyo, Komaba, Meguro-ku, Tokyo

(Received March 11, 1967)

Abstract:

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)-α above the transition point Tc, it should have a singularity C-(Tc-T)-α below Tc, C- being not necessarily equal to C+.
(b) If the specific heat has a logarithmic singularity -Aln (T-Tc)+B+ above Tc, it should have a singularity -Aln (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.


URL : http://ptp.ipap.jp/link?PTP/38/322/
DOI : 10.1143/PTP.38.322

[ Full Text PDF : FREE ACCESS (596K) ] Citation:

References:

  1. R. Abe, Prog. Theor. Phys. 37 (1967), 1070[PTP].
  2. M. E. Fisher, Lectures in Theoretical Physics (University of Colorado Press, Boulder, 1964), Vol. 7c, p. 1.
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Citing Article(s) :

  1. Journal of the Physical Society of Japan 58 (1989) pp. 4344-4351 :
    Phase Boundary of an Ising Antiferromagnet
    S. Dasgupta
  2. Progress of Theoretical Physics Vol. 38 No. 5 (1967) pp. 1182-1183 :
    Zeros of Partition Function for the Husimi-Temperley Model
    Ryuzo Abe
  3. Progress of Theoretical Physics Vol. 38 No. 6 (1967) pp. 1243-1251 :
    Note on Singularity of Specific Heat in the Second Order Phase Transition
    Masuo Suzuki
  4. Progress of Theoretical Physics Vol. 40 No. 6 (1968) pp. 1246-1256 :
    Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism
    Masuo Suzuki
  5. 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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