Asymptotic States of Ising Ferromagnets with Long-range Interactions

TL;DR

This study explores how long-range interactions influence the relaxation dynamics and metastable states of two-dimensional Ising ferromagnets, revealing that such interactions suppress striped metastable states at zero temperature in finite systems and accelerate ordering at non-zero temperatures.

Contribution

It provides new insights into the effects of power-law long-range interactions on the relaxation and metastability of 2D Ising ferromagnets through Monte Carlo simulations.

Findings

Long-range interactions suppress striped metastable states at T=0 in finite systems.

In the thermodynamic limit, the occurrence of striped states aligns with short-range behavior.

At T≠0, the system always reaches an ordered final state more quickly with stronger 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.