Prog. Theor. Phys. Vol. 67 No. 1 (1982) pp. 118-130
Gaussian Random Bond Problem for Annealed System in 1/n Expansion
* Department of Pure and Applied Sciences, University of Tokyo, Komaba, Tokyo 153
**Theoretical Physics Institute and Department of Physics, University of Alberta, Edmonton, T6G 2J1
(Received June 10, 1981)
Critical phenomena for the for the annealed n-vector model are studied in 1/n expansion by assuming that the exchange interactions between spins are fluctuating variables obeying the Gaussian distribution. It is shown that for an overall fluctuation of the interaction between spins the susceptibility never diverges at any finite temperature except for n→∞ (spherical limit) and n=1 (Ising) cases.
On the other hand, if the fluctuation is restricted to only nearest-neighbor pairs, the susceptibility is proved to diverge at an appropriate transition temperature in the limit n→∞. The critical exponent γ in this case is shown to be the same as the spherical model value. Also the dependence of transition temperature on the strength of fluctuation is discussed.
DOI : 10.1143/PTP.67.118
- R. Abe, Prog. Theor. Phys. 59 (1978), 742[PTP].
- K. Ideura, Y. Okabe and R. Abe, Prog. Theor. Phys. 65 (1981), 1179[PTP].
- M. Oku, Prog. Theor. Phys. 66 (1981), 77[PTP].
- R. Abe, Prog. Theor. Phys. 49 (1973), 113[PTP].
- R. Abe and S. Hikami, Prog. Theor. Phys. 57 (1977), 1197[PTP].
- K. Husimi, Proceedings of the International Conference of Theoretical Physics, Kyoto and Tokyo, 1953, p. 531.
H. N. V. Temperley, Proc. Phys. Soc. A 67 (1954), 233.
D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. 35 (1975), 1792[APS].
S. Kirkpatrick and D. Sherrington, Phys. Rev. B 17 (1978), 4384[APS].
Y. Okabe and M. Masutani, Phys. Lett. A 65 (1978), 97[CrossRef].
Y. Okabe and M. Masutani, preprint received in July, 1981.
T. H. Berlin and M. Kac, Phys. Rev. 86 (1952), 821[APS].
H. E. Stanley, Phys. Rev. 176 (1968), 718[APS].
M. N. Barber and M. E. Fisher, Ann. of Phys. 77 (1973), 1[CrossRef].
S. Hikami and R. Abe, Prog. Theor. Phys. 55 (1976), 1472[PTP].
M. F. Thorpe and D. Beeman, Phys. Rev. B 14 (1976), 188[APS].
Citing Article(s) :
Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 2176-2179
Phase Diagram in the Large N Limit of the Annealed N-Vector Model with Gaussian Random Bonds and Its Relation to the RPN-1 Model