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Slow relaxation in the Ising model on a small-world network with strong long-range interactions

Daun Jeong·M. Y. Choi·Hyunggyu Park
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Abstract

We consider the Ising model on a small-world network, where the long-range interaction strength $J_2$ is in general different from the local interaction strength $J_1$, and examine its relaxation behaviors as well as phase transitions. As $J_2/J_1$ is raised from zero, the critical temperature also increases, manifesting contributions of long-range interactions to ordering. However, it becomes saturated eventually at large values of $J_2/J_1$ and the system is found to display very slow relaxation, revealing that ordering dynamics is inhibited rather than facilitated by strong long-range interactions. To circumvent this problem, we propose a modified updating algorithm in Monte Carlo simulations, assisting the system to reach equilibrium quickly.

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Daun Jeong, M. Y. Choi, Hyunggyu Park. 2005-01-06. Slow relaxation in the Ising model on a small-world network with strong long-range interactions. https://doi.org/10.1103/physreve.71.036103

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