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Progress of Theoretical Physics Supplement

Phase Transition of Two-Dimensional Diluted XY and Clock Models

Yutaka Okabe, Tasrief Surungan

Published Jan 1, 2005• 2 citations
Publisher

Abstract

We study the two-dimensional bond-diluted XY and 6-state clock models by Monte Carlo simulation with cluster spin updates. We show that with dilution the KT transition temperature approaches zero at the percolation threshold, and the decay exponent at the KT temperature is universal, that is, &eegr;= 1/4. For the 6-state clock model, we observe a systematic shift of lower critical temperature due to the discrete symmetry. The universal behavior of the decay exponent at the lower KT temperature is also shown.

DOI
10.1143/ptps.157.132

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We study the two-dimensional bond-diluted XYXYXY and six-state clock models by Monte Carlo simulation with cluster spin updates. Various concentrations of depleted bonds were simulated, in which we found a systematic decrease of the Kosterlitz-Thouless (KT) transition temperatures of both XYXYXY and six-state clock models as the concentration of dilution decreases. For the six-state clock model, a second KT transition at lower temperature was observed. The KT transition temperatures as well as the decay exponent $\ensuremath{\eta}$ for each concentration of dilution are estimated. It is observed that the quasi-long-range order disappears at the concentration of dilution very close to the percolation threshold. The decay exponent $\ensuremath{\eta}$ of the KT transitions calculated at each concentration indicates that the universality class belongs to the pure XYXYXY and clock models, analogous to the expectation of the Harris criterion for the irrelevance of randomness in the continuous phase transition of systems with nondiverging specific heat.
The critical behavior of the clock model in two-dimensional square lattice is studied numerically using Monte Carlo method with Wolff algorithm. The Kosterlitz-Thouless (KT) transition is observed in the six-state clock model, where an intermediate phase exists between the low-temperature ordered phase and the high-temperature disordered phase. The bond randomness is introduced to the system by assuming a Gaussian distribution for the coupling coefficients with the mean μ=1 and different values of variance, from σ2=0.1 to σ2=3.0. An abrupt jump in the helicity modulus at the transition, which is the key characteristic of the KT transition, is verified with a stability argument. The critical temperature Tc for both pure and disordered systems is determined from the critical exponent η(Tc)=1/4. The results showed that a small amount of disorder (small σ) reduces the critical temperature of the system, without altering the nature of transition. However, a larger amount of disorder changes the transition from the KT-type into that of non-KT-type.
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