Prog. Theor. Phys. Vol. 63 No. 4 (1980) pp. 1121-1136

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A Path-Integral Approach to the X-Y Model in One- and Two-Dimensions

— Dynamics and Quantum Effects at Low Temperatures —

Satoshi Takada

Institute of Physics, University of Tsukuba, Ibaraki 305

(Received October 22, 1979)

Abstract:

The X-Y model in one- and two-dimensions is investigated by means of the path integral. The low temperature properties are shown to be described by the phase mode. In particular, the quantum model in the limit S→∞ is found to be well expressed by the planer model. The spin-correlation functions are calculated explicitly. As a result it is found that at zero temperature the quasi long-range order in one-dimension and the long-range order in two-dimensions appear. The spontaneous magnetization is explicitly given at zero temperature in two-dimensions. At finite temperatures the dynamical behaviour is the same as that studied by Nelson and Fisher. The divergence of the susceptibility at T = 0 in one-dimension is shown to be different from that of the classical model.

URL : http://ptp.ipap.jp/link?PTP/63/1121/
DOI : 10.1143/PTP.63.1121

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Citing Article(s) :

Journal of the Physical Society of Japan 64 (1995) pp. 1955-1966 :
Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

Hiroaki Nakamura, Naomichi Hatano and Minoru Takahashi
Progress of Theoretical Physics Vol. 65 No. 5 (1981) pp. 1595-1602 :
Monte Carlo Simulation of the Plane Rotator Model. III

Seiji Miyashita