Critical exponents of the 3D antiferromagnetic three-state Potts model using the coherent-anomaly method

Abstract

The antiferromagnetic three-state Potts model on the simple-cubic lattice is studied using the coherent-anomaly method (CAM). The CAM analysis provides the estimates for the critical exponents which indicate the XY universality class, namely α = −0.011, β = 0.351, γ = 1.309 and δ = 4.73. This observation corroborates the results of the recent Monte Carlo simulations, and disagrees with the proposal of a new universality class.

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

“…A few previous theories predicted the presence of multiple phase transitions in a model related to ours, [23][24][25][26][27][28][29][30][31][32] but our result is not consistent with their prediction. The system size dependence of this peak is shown in the inset of Fig.…”

“…As explained before, the antiferro 3-state Potts model is a much simpler model that has the same symmetry with our models; each microscopic pseudospin can point to only three directions, which corresponds to the limit of c → ∞ in the model (7). Although there have been a pile of studies about this problem for the Potts case on bipartite lattices, [23][24][25][26][27][28][29][30][31] several important points are not settled down about this model. Most importantly, the nature of the ordered states has not been well clarified for the Potts case.…”

“…Most importantly, the nature of the ordered states has not been well clarified for the Potts case. [23][24][25][26][27][28][29][30][31][32] The consensus is that the lowest-temperature phase is the broken sublattice-symmetry (BSS) state. 23) This is the phase in which the symmetry between the two sublattices is broken and this may also be called a ferri state.…”

“…Inside this phase the sublattice moments uniformly fluctuate. 26,28) We will examine the following two points in our rotor model (7). The first one is about the nature of the lowtemperature ordered phase.…”

“…23) However, their results are not consistent to each other about the ordered phases, and the nature of the ordered states has not been well clarified. [23][24][25][26][27][28][29][30][31][32] In our models, microscopic degrees of freedom of local order parameters are enlarged from three points in the Potts model, and can be located a unit circle (one-dimensional compact manifold) or a two-dimensional continuous vector space (twodimensional noncompact manifold). This corresponds to coarse graining processes of the Potts model, and we expect that our models exhibit the nature of order parameter configuration more clearly.…”