  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.
