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Journal of the Physical Society of Japan

Thermodynamic Properties of Antiferromagnetic QuantumXY-Model on the Triangular Lattice

Shigeo Homma, Hirotsugu Matsuda, N. Ogita, Kazuhiro Sano

Published Mar 15, 1993• 2 citations
Publisher

Abstract

Thermodynamic properties of antiferromagnetic quantum X Y -model ( s =1/2) on a triangular lattice are studied by the Decoupled Cell Monte Carlo Method (DCM). The decoupled cell (DC) used in this study consists of 7 spins. The size N of systems are 15 * 15, 30 * 30, 45 * 45, respectively. Detailed studies of spin pair correlation functions for both x - and z -components are performed at various temperatures. The results suggest that the existence of the shortrange three sublattice structure. The mean square magnetization of a sublattice for the x -component does not depend on N , whereas that of the z -component shows a strong dependence on N below a certain temperature.

DOI
10.1143/jpsj.62.880

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Decoupled cell method is introduced as a method of Monte Carlo simulation for quantum spin systems. Based on this method we calculated the thermodynamic quantities such as an internal energy, in-plane and out-of-plane susceptibilities and spin-spin correlation functions in one dimensional XY model. The agreement with the exact results is excellent above a certain demarcation temperature. This method is also applied to the antiferromagnetic Heisenberg model on the triangular lattice. The results indicate the existence of a sublattice structure composed of three sublattices, although its spatial and temporal behaviours are short ranged.
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The thermodynamic properties and phase transitions in a two-dimensional strongly diluted threevertex antiferromagnetic Potts model on a triangular lattice have been investigated using the Monte Carlo method. The systems with linear dimensions of L × L = N , where L = 18–48, have been considered. It has been shown using the method of fourth-order Binder cumulants that, upon the introduction of nonmagnetic impurities into the spin system described by the two-dimensional antiferromagnetic Potts model, the firstorder phase transition changes to a second-order phase transition.
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