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

Abstract

Based on a Renormalization-Group picture of Zn symmetric models in three dimensions, we derive a scaling law for the Zn order parameter in the ordered phase. An existing Monte Carlo calculation on the three-state antiferromagnetic Potts model, which has the effective Z6 symmetry, is shown to be consistent with the proposed scaling law. It strongly supports the Renormalization-Group picture that there is a single massive ordered phase, although an apparently rotationally symmetric region in the intermediate temperature was observed numerically.75.10.Hk, 05.50+q

Classical Monte Carlo Study for Antiferro Quadrupole Orders in a Diamond Lattice

“…In the renormalization-group processes, the effects of the anisotropy become strongly suppressed near the critical fixed point but start to grow as the system approaches the low-temperature fixed point. 38,39) There, the macroscopic degeneracy inherent in the antiferro 3-state Potts model is lifted, and the Z 3 symmetry is broken together with the Z 2 sublattice symmetry. Remember that the "3" in Z 3 corresponds to the three minima in the potential energy due to the 3-fold anisotropy.…”

Ordered phase and phase transitions in the three-dimensional generalized six-state clock model

“…The high temperature phase transition in Z 6 models belongs to the 3D-XY universality class [14]. Indeed, the transitions in the 3D-3AFP model [15] and the six-state clock model [3] are found to belong to the 3D-XY universality class.…”

“…Next, following the idea of Oshikawa [14] for the 3D-3AFP model, we make the finite size scaling plots of − cos 6θ by ordinary Monte Carlo method on lattices L = 12, 18, 24 and 30. Here, − cos 6θ is the order parameter for the Z 6 symmetry breaking and θ is the angle of magnetization from one of the COP states.…”

“…Recent theoretical and numerical studies on the 3D-3AFP model have revealed that the existence of these phases are fake owing to the finite size effect [14][15][16]. There is only a low-temperature phase that corresponds to the IOP1.…”

Nature of the possible magnetic phases in a frustrated hyperkagome iridate

“…Low-T physics of the Potts model are controlled by 3D XY fixed point, T = 0 Nambu-Goldstone (NG) fixed point and T = 0 fixed point with large Z 6 term. 33,34 The critical point (T = T c ) belongs to the XY fixed point, below which all the renormalization group (RG) flow goes to the large Z 6 fixed point. 33 The U(1) to Z 6 crossover below T c stems from the dangerously irrelevant behavior of the Z 6 anisotropy term.…”