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Prog. Theor. Phys. Vol. 38 No. 1 (1967) pp. 72-80

[ Full Text PDF : FREE ACCESS (496K) ]

Note on the Critical Behavior of Ising Ferromagnets

Ryuzo Abe

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

(Received April 3, 1967)

Abstract:

Behavior of Ising ferromagnets near the transition point in the presence of magnetic field is studied by means of the Lee-Yang theorem on the distribution of zeros of partition function. Relations for the critical indices so far obtained by several authors are rederived by the present method, and some discussions are given of the dependence of thermodynamic quantities at the transition point on magnetic field.


URL : http://ptp.ipap.jp/link?PTP/38/72/
DOI : 10.1143/PTP.38.72

[ Full Text PDF : FREE ACCESS (496K) ] Citation:

References:

  1. R. Abe, Prog. Theor. Phys. 37 (1967), 1070[PTP].
  2. R. Abe, Prog. Theor. Phys., to be published.
  3. See, for example, M. E. Fisher, Lectures in Theoretical Physics (University of Colorado Press, Boulder, 1964), Vol. 7c, p. 1.
  4. C. Domb and D. L. Hunter, Proc. Phys. Soc. 86 (1965), 1147.
    C. Domb, Proceedings of the 1966 Low Temperature Calorimetry Conference, edited by O. V. Lounasmaa, Ann. Acad. Sci. Fennicae A VI (1966), 167.
  5. M. Suzuki, J. Phys. Soc. Jpn. 22 (1967), 757[JPSJ].
  6. T. D. Lee and C. N. Yang, Phys. Rev. 87 (1952), 410[APS].
  7. J. W. Essam and M. E. Fisher, J. Chem. Phys. 38 (1963), 802[CrossRef].
  8. G. S. Rushbrooke, J. Chem. Phys. 39 (1963), 842[AIP Scitation].
  9. R. B. Griffiths, J. Chem. Phys. 43 (1965), 1958[CrossRef].
  10. B. Widom, J. Chem. Phys. 43 (1965), 3898[CrossRef].
  11. L. P. Kadanoff, Physics 2 (1966), 263.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 38 No. 1 (1967) pp. 289-290 :
    A Theory on the Critical Behaviour of Ferromagnets
    Masuo Suzuki
  2. Progress of Theoretical Physics Vol. 38 No. 3 (1967) pp. 568-575 :
    Critical Behavior of Pair Correlation Function in Ising Ferromagnets
    Ryuzo Abe
  3. Progress of Theoretical Physics Vol. 38 No. 5 (1967) pp. 1182-1183 :
    Zeros of Partition Function for the Husimi-Temperley Model
    Ryuzo Abe
  4. 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
  5. 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
  6. Progress of Theoretical Physics Vol. 39 No. 2 (1968) pp. 349-364 :
    A Theory of the Second Order Phase Transitions in Spin Systems. III
    Masuo Suzuki
  7. Progress of Theoretical Physics Vol. 40 No. 6 (1968) pp. 1246-1256 :
    Theorems on Extended Ising Model with Applications to Dilute Ferromagnetism
    Masuo Suzuki
  8. Progress of Theoretical Physics Vol. 41 No. 6 (1969) pp. 1438-1449 :
    On the Distribution of Zeros for the Heisenberg Model
    Masuo Suzuki
  9. Progress of Theoretical Physics Vol. 42 No. 5 (1969) pp. 1076-1085 :
    Singularity of Nonlinear Response near the Critical Field. I
    Masuo Suzuki
  10. Progress of Theoretical Physics Vol. 43 No. 4 (1970) pp. 882-906 :
    On the Singularity of Dynamical Response and Critical Slowing Down
    Masuo Suzuki
  11. Progress of Theoretical Physics Vol. 44 No. 2 (1970) pp. 339-347 :
    Some Remarks on Perturbation Theory and Phase Transition with an Application to Anisotropic Ising Model
    Ryuzo Abe
  12. Progress of Theoretical Physics Vol. 49 No. 4 (1973) pp. 1096-1105 :
    Critical Exponents and Scaling Relations in 1/n Expansion. II
    Shinobu Hikami

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