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

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.

13 pages, 6 figures

References in corpus (5)

• Order-N Cluster Monte Carlo Method for Spin Systems with Long-range Interactions
• Monte Carlo studies of the one-dimensional Ising spin glass with power-law interactions
• Kosterlitz-Thouless transition in planar spin models with bond dilution
• Effect of magnetoelastic coupling on spin-glass behavior in Heisenberg pyrochlore antiferromagnets with bond disorder
• The ordered phase of the one-dimensional Ising spin glass with long-range interactions

Cited by in corpus (2)

• Critical Nonequilibrium Cluster-flip Relaxations in Ising Models
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality