Relaxational processes in the one-dimensional Ising model with long-range interactions

TL;DR

This study uses Monte Carlo simulations to explore relaxational dynamics in one-dimensional long-range Ising models, revealing complex droplet behavior influenced by effective dimension and interaction decay.

Contribution

It provides a systematic analysis of droplet dynamics across different effective dimensions in long-range 1D Ising models, connecting numerical results with droplet theory.

Findings

Droplet surface dimension is distributed around the effective dimension.

Distribution of surface dimensions enhances dynamical crossover.

Droplet dynamics vary with the decay parameter $\sigma$.

Abstract

Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter $\sigma$, which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of $\sigma$. Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover.