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

Abstract

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)/|J(1| > 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 → ∞. 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 </~1.

Duality between the Deconfined Quantum-Critical Point and the Bosonic Topological Transition

“…This issue is discussed with examples from classical systems in Ref. [72]. Here, we do not see any evidence of a fast divergence of the peak value; thus, the transition should still be continuous.…”

Nematic phase in theJ1−J2square-lattice Ising model in an external field

“…In the most recent studies combining Monte Carlo simulations and a series of analytical techniques it has been established that the line of phase transitions in the temperature versus κ plane is first order for 1/2 < κ < 0.67 and is continuous with Ashkin-Teller critical behavior for κ > 0.67. The critical exponents change continuously in this regime between the four-state Potts model behavior at κ = 0.67 to standard Ising criticality for κ → ∞ [20,21]. In the square approximation, the CVM variational free energy …”

“…In this work we consider J 1 < 0 and J 2 > 0 representing ferromagnetic NN and antiferromagnetic NNN interactions respectively. The competition ratio is defined by κ = At zero external field the model has been extensively studied [14][15][16][17][18][19][20][21][22], considering both ferromagnetic J 1 < 0 and antiferromagnetic J 1 > 0 NN interactions and antiferromagnetic J 2 > 0 NNN interactions. The nature of the thermal phase transition from the stripes to a disordered phase for κ > 1/2 was controversial.…”

Dynamic approach to finite-temperature magnetic phase transitions in the extendedJ1−J2model with vacancy order

“…However, even for the frustrated Ising model without vacancies, it is difficult to precisely determine the order and the universality class of the phase transitions. [49,50] In this respect, the short-time dynamic approach [51,52] can be utilized. Recent activities include various applications and developments [53,54] such as theoretical and numerical studies of the Josephson-junction arrays [55] and ageing phenomena [56,57].…”