Interface Approach to Phase Transitions and Ordering by Monte Carlo Simulations and Its Applications to Three-Dimensional Antiferromagnetic Potts Models

Two Types of Ordering in the Three-State Antiferromagnetic Potts Model on 3D Lattices: Monte Carlo Evidence

“…1a around the y axis) with a radius increasing with decreasing temperature. Apparently, the relevant order parameter in the critical region close to T c would be z r , which actually was used for the susceptibility calculations in previous MC calculations [4,5,11]. This result is consistent with the reported XY universality class: The free energy of the XY model is rotationally symmetric in ͗s x ͘, ͗s y ͘ space at any temperature.…”

Antiferromagnetic Potts models on the square lattice

“…( which is satisfied by the numerical estimates β trans (SC q = 3 Potts AF) ≈ 0.816 [11,81,82,83,84], β trans (SC q = 4 Potts AF) ≈ 1.43 [85], and β crit (SC Ising ferro) ≈ 0.222 [86]. The goal of this Appendix is to prove the following theorem:…”

Ordered phase and scaling inZnmodels and the three-state antiferromagnetic Potts model in three dimensions

“…On the other hand, according to numerical calculations, there appears to be an intermediate phase below T c and above the low-temperature phase. While there have been various proposals [5][6][7] for the intermediate region, most reliable numerical results at present indicates that the intermediate region appears to be rotationally symmetric phase which is similar to the ordered phase of the 3D XY model [10][11][12] . However, the "transition" between the intermediate region and the low-temperature phase is not well understood.…”