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

Yusuke Tomita
Phys. Rev. E 94, 062142 – Published 28 December 2016

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 σ, 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 σ. 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.

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  • Received 22 September 2015
  • Revised 26 November 2016

DOI:https://doi.org/10.1103/PhysRevE.94.062142

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Yusuke Tomita

  • College of Engineering, Shibaura Institute of Technology, Minuma-ku, Saitama 337-8570, Japan

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Issue

Vol. 94, Iss. 6 — December 2016

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