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.

References in corpus (8)

• Winding angle variance of Fortuin-Kasteleyn contours
• Zero-Temperature Relaxation of Three-Dimensional Ising Ferromagnets
• Zero-Temperature Freezing in Three-Dimensional Kinetic Ising Model
• Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures
• Coarsening in inhomogeneous systems
• Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model
• Coarsening and percolation in a disordered ferromagnet
• Coexistence of coarsening and mean field relaxation in the long-range Ising chain

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• Domain Growth in Long-range Ising Models with Disorder
• Harnessing finite-size effects to gauge aging in the $2D$ Ising model