Ashkin-Teller Criticality and Pseudo-First-Order Behavior in a Frustrated Ising Model on the Square Lattice

We study the challenging thermal phase transition to stripe order in the frustrated square-lattice Ising model with couplings J(1) < 0 ( nearest-neighbor, ferromagnetic) and J(2) > 0 ( second-neighbor, antiferromagnetic) for g = J(2)/vertical bar J(1)vertical bar > 1/2. Using Monte Carlo simulations and known analytical results, we demonstrate Ashkin-Teller criticality for g >= g*; i.e., the critical exponents vary continuously between those of the 4-state Potts model at g = g* and the Ising model for g -> infinity. Thus, stripe transitions offer a route to realizing a related class of conformal field theories with conformal charge c = 1 and varying exponents. The transition is first order for g < g* = 0.67 +/- 0.01, much lower than previously believed, and exhibits pseudo-first-order behavior for g* <= g less than or similar to 1.