Novel criticality in a simple three-dimensional Potts model with next-nearest-neighbor interaction

We investigate the antiferromagnetic Potts model on the cubic lattice with a next-nearest-neighbor ferromagnetic interaction J'. 

In the weak J' region, the next-nearest term induces a two-step symmetry breaking with the final ground state being 12-fold degenerate. 

The J' term does not affect the criticality of the higher temperature phase transition, which we show matches the cubic-anisotropic Heisenberg universality for the J'=0 case, contrary to what has been claimed previously [1]. However, it changes the symmetry being broken to four-state ferromagnetic Potts, which has a first-order transition. We analyze the transition with Wolff cluster update MCMC, and discuss the possible slight discrepancies in the critical exponents. 

A polytope called a "cuboctahedron" can be constructed from the 12 degenerate ordered states by their relative relation [2]. This polytope, being closer to a sphere compared to a cube, leads us to expect an emergent O(3) symmetry at a single critical point when the two-step phase transitions coincide. However, this scenario is avoided by a fluctuation-induced first order transition, which we will discuss in the talk as well. 

[1] C. Yamaguchi & Y. Okabe, J. Phys. A 34, 8781 (2001).

[2] J. Takahashi & A. W. Sandvik, Phys. Rev. Research 2, 033459 (2020).