Probability-changing cluster algorithm for two-dimensional (formula presented) and clock models

We extend the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm to the study of systems with the vector order parameter. Wolff’s idea of the embedded cluster formalism is used for assigning clusters. The Kosterlitz-Thouless (KT) transitions for the two-dimensional (2D) (formula presented) and q-state clock models are studied by using the PCC algorithm. Combined with the finite-size scaling analysis based on the KT form of the correlation length, (formula presented) we determine the KT transition temperature and the decay exponent (formula presented) as (formula presented) and (formula presented) for the 2D (formula presented) model. We investigate two transitions of the KT type for the 2D q-state clock models with (formula presented) and confirm the prediction of (formula presented) at (formula presented) the low-temperature critical point between the ordered and (formula presented)-like phases, systematically.