Numerical study of the phase transitions in the two-dimensional Z(5) vector model

Abstract

We investigate the critical properties of the two-dimensional Z(5) vector model. For this purpose, we propose a cluster algorithm, valid for Z(N) models with odd values of N. The two-dimensional Z(5) vector model is conjectured to exhibit two phase transitions with a massless intermediate phase. We locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices and compare the results with analytical predictions.

Stochastic resonance in the two-dimensionalq-state clock models

“…The temperature T is given in units of J/kB, where kB is the Boltzmann constant, and the vertical lines indicate Tc1 and Tc2 in the thermodynamic limit, respectively, estimated in Ref. [13]. As the system size increases, τ −1 vanishes in the quasiliquid phase between Tc1 and Tc2, where m = me iφ may freely wander around in the angular direction.…”

Critical properties of 2D Z(N) vector models for N>4

“…Considering the determinations of the critical coupling β (1,2) c (N) obtained in this work for N = 7 and 17, together with those obtained for N = 5 in Refs. [7,8] and those for N = 6, 8 and 12 of Ref. [6], one can verify that β (1) c (N) approaches the 2D XY value, β (1) c = 1.1199, exponentially in N or even faster, while β (2) c (N) grows to infinity with N 2 .…”

“…(1.1) using the same cluster Monte Carlo algorithm adopted in the Refs. [7,8] for the case N = 5. We used several different observables to probe the two expected phase transitions.…”

“…We observe that the hyperscaling relation γ/ν + 2β /ν = d = 2 is nicely satisfied within statistical errors in both models. We can cross-check our determination of the critical exponent η by an independent method, which does not rely on the prior knowledge of the critical coupling, but is based on the construction of a suitable universal quantity [12,8]. The idea is to plot…”

“…[7,8] we have started a detailed numerical investigation of the BKT transition in 2D Z(N) models for N = 5 which is the lowest number where this transition can occur. Our findings support the scenario of two BKT transitions with conventional critical indices.…”