Asymptotic States of Ising Ferromagnets with Long-range Interactions

Abstract

It is known that, after a quench to zero temperature ($T=0$), two-dimensional ($d=2$) Ising ferromagnets with short-range interactions do not always relax to the ordered state. They can also fall in infinitely long-lived striped metastable states with a finite probability. In this paper, we study how the abundance of striped states is affected by long-range interactions. We investigate the relaxation of $d=2$ Ising ferromagnets with power-law interactions by means of Monte Carlo simulations at both $T=0$ and $T\ne 0$. For $T=0$ and the finite system size, the striped metastable states are suppressed by long-range interactions. In the thermodynamic limit, their occurrence probabilities are consistent with the short-range case. For $T\ne 0$, the final state is always ordered. Further, the equilibration occurs at earlier times with an increase in the strength of the interactions.

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• Critical clusters in liquid crystals: Fractal geometry and conformal invariance
• Critical dynamics of long range models on Dynamical Lévy Lattices
• Domain Growth in Long-range Ising Models with Disorder
• Harnessing finite-size effects to gauge aging in the $2D$ Ising model