132 Progress of Theoretical Physics Supplement No. 157, 2005 Phase Transition of Two-Dimensional Diluted XY and Clock Models

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, η = 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. The effect of dilution on the phase transition has been extensively studied. In a pioneering work, Harris1) studied the problem whether the randomness changes the critical behavior of the pure system in the case of quenched random systems. The so-called Harris criterion1) states that the dilution will be relevant (irrelevant) if th