Ashkin-Teller criticality and weak-first-order behavior of phase transition to four-fold degenerate state in two-dimensional frustrated Ising antiferromagnets

We study the thermal phase transitions of the four-fold degenerate phases (the plaquette and single stripe states) in two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the parameter regions with the plaquette and single stripe phases, respectively. The four-state Potts-critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size scaling analyses. Furthermore, similar behavior of the transition to the four-fold single stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the four-fold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.