Two-Dimensional Ising Model with Competing Interactions as a Model for Interacting π-Rings

Abstract

We investigate the Ising model on a square lattice with antiferromagnetic exchange between nearest and next-nearest neighbors and show that at low temperatures stripe-like and droplet-like superstructures appear. We show that the competing interactions introduce a strong frustration that could plausibly describe the systems with dipole-dipole type interactions and pay particular attention to arrays of interacting Josephson π-rings.

The role of long relaxation times in a simple model with massless modes

“…Ising model with competing interactions has previously been discussed by O'Hare et al [24,25] whose The results in Sect. III indicate that the nnn Ising model exhibits a glass-like transition (τ * → ∞ when T ≤ T g ) only for a special choice of the model parameters, i.e.…”

“…A remaining question is the precise behaviour of the order-disorder phase transition lines as the critical value of K is approached. Some previous authors provide a phase diagram that show the order-disorder transition lines continuously approaching T = 0 with a finite slope [19,25].…”