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Prog. Theor. Phys. Vol. 49 No. 5 (1973) pp. 1451-1458

Critical Behavior of the Anisotropic Classical n-Vector Model

Masuo Suzuki

Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo

(Received November 13, 1972)

Abstract:

The critical exponents of the anisotropic classical model with n components are investigated in the 1/n-expansion. It is found that they depend only upon the number of the spin components with the largest interaction. This gives a partial confirmation of the universality. It is also proved that the singular part of the derivative of the perpendicular susceptibility is proportional to the dominant singularity of the specific heat through the first order of 1/n: i.e., γ_⊥=α-1+O(1/n²).

URL : http://ptp.ipap.jp/link?PTP/49/1451/
DOI : 10.1143/PTP.49.1451

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References:

1. M. Suzuki, Phys. Lett. A 42 (1972), 5[CrossRef]; Prog. Theor. Phys. 49 (1973), 424 [PTP](to be referred to as I).
2. M. Suzuki, Prog. Theor. Phys. 49 (1973), 1106 [PTP](to be referred to as II).
3. M. Suzuki, Prog. Theor. Phys. 49 (1973), 1440 [PTP](to be referred to as III).
4. R. Abe, Prog. Theor. Phys. 48 (1972), 1414[PTP]; ibid. 49 (1973), 113[PTP].
   R. Abe and S. Hikami, Prog. Theor. Phys. 49 (1973), 442[PTP].
   S. Hikami, Prog. Theor. Phys. 49 (1973), 1096[PTP].
5. S. Ma, Phys. Rev. Lett. 29 (1972), 1311[APS]; Phys. Rev. A 7 (1973), 2172[APS].
6. M. E. Fisher and P. Pfeuty, Phys. Rev. B 6 (1972), 1889[APS].
7. K. G. Wilson, Phys. Rev. Lett. 28 (1972), 548[APS].
8. M. E. Fisher, Rep. Prog. Phys. 30 (1967), 615[CrossRef].
9. M. Suzuki, Prog. Theor. Phys. 46 (1971), 1054[PTP].
10. H. E. Stanley, Phys. Rev. 176 (1968), 718[APS].
11. K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28 (1972), 240[APS].
12. M. Suzuki, Phys. Rev. Lett. 28 (1972), 508[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 50 No. 2 (1973) pp. 393-408 :

   On the Expansion Theory of Critical Exponents

   Masuo Suzuki

2. Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 1085-1086 :

   On the Critical Behavior of the Two-Dimensional Heisenberg-Ising Model

   Masuo Suzuki and Fumihiko Tanaka

3. Progress of Theoretical Physics Vol. 50 No. 3 (1973) pp. 1097-1098 :

   Calculation of the Cross-Over Exponent by Using Callan-Symanzik Equations

   Yoshitake Yamazaki and Masuo Suzuki

4. Progress of Theoretical Physics Vol. 52 No. 2 (1974) pp. 369-378 :

   Crossover Exponent of the Spin Anisotropic n-Vector Model with Short-Range Interaction in 1/n Expansion

   Shinobu Hikami and Ryuzo Abe

5. Progress of Theoretical Physics Vol. 52 No. 5 (1974) pp. 1431-1437 :

   Critical Behavior of an Extremely Anisotropic n-Vector Model

   Shinobu Hikami

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