Prog. Theor. Phys. Vol. 62 No. 4 (1979) pp. 927-935

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Magnetic Correlation Function of the Two-Dimensional Planar Spin Model

— Self-Consistent Calculation —

Yukio Saito

Institut für Festkörperforschung der Kernforschungsanlage Jülich, 5170 Jülich, Fed. Rep. Germany

(Received February 19, 1979)

Abstract:

The magnetic correlation function g(r) of the Villain model is calculated by applying the dual transformation to the discrete Gaussian (DG) model and by approximating it by the modified discrete Gaussian (mDG) model. g(r) decays with a power law with an exponent η below the critical temperature T_c, which corresponds to the roughening point in the mDG model. The susceptibility χ is infinite below T_c. Above T_c, g(r) decays exponentially with a magnetic correlation length ξ_M, which behaves similarly to the height correlation length ξ in mDG model: ln ξ_M ∼(1-T_c/T)^-\tildeν with the exponent \tildeν=1. The susceptibility χ is proportional to ξ^{2- η(T)}_M, where the exponent η takes the value 1/4 at T_c. The value η(T_c)=1/4 agrees with that by Kosterlitz or the experimental results, although the value \tildeν=1 is different from \tildeν=1/2 obtained by Kosterlitz.
Step free energy and the height difference correlation function in the mDG model are also calculated.

URL : http://ptp.ipap.jp/link?PTP/62/927/
DOI : 10.1143/PTP.62.927

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Citing Article(s) :

Progress of Theoretical Physics Vol. 63 No. 3 (1980) pp. 831-841 :
Commensurate-Incommensurate Transition and Melting in Two-Dimension

Yukio Saito
Progress of Theoretical Physics Vol. 89 No. 2 (1993) pp. 545-549 :
A New Possible Approach in Kosterlitz-Thouless Transitions

Xiao Hu