Wang-Landau study of first-order and Berezinskii-Kosterlitz-Thouless transitions in classical spin models

Abstract

We investigate phase transitions and critical behavior in the two-dimensional Blume-Capel model and the six-state clock model by using the Wang-Landau sampling method including the parallel replica-exchange variant. First, in the Blume-Capel model examined up to the lattice size of 48x48 sites, we construct the first-order transition line with much improved accuracy and resolution, finding out a double-peak structure of specific heat where diverging phase-transition peak and the system-size independent Schottky-like peak appears together. Throughout the phenomenological finite-size-scaling analysis at the tricritical point, we also provide the first Wang-Landau examination on the conjecture of the exact tricritical eigenvalue exponents, yt = 9/5, yg = 4/5, and yh = 77/40. Second, we perform the parallel replica-exchange Wang-Landau calculations on the six-state clock model. We identify the Berezinskii-Kosterlitz-Thouless (BKT) transitions by directly calculating the helicity modulus. The nature of the BKT transitions is further characterized in the map of the Fisher zeros of the partition function. We find that a single leading zero or a discrete impact angle does not exist and the whole line of zeros in the critical area approaches the real axis with the same system-size scaling.