Survival of short-range order in the Ising model on negatively curved surfaces

2009/06/30 by Yasunori Sakaniwa, Hiroyuki Shima, Sakaniwa, Yasunori +1 · 1 citation
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Markov Chains and Monte Carlo Methods

paper · pdf · doi:10.48550/arxiv.0906.5523

Abstract

We examine the ordering behavior of the ferromagnetic Ising lattice model defined on a surface with a constant negative curvature. Small-sized ferromagnetic domains are observed to exist at temperatures far greater than the critical temperature, at which the inner core region of the lattice undergoes a mean-field phase transition. The survival of short-range order at such high temperatures can be attributed to strong boundary-spin contributions to the ordering mechanism, as a result of which boundary effects remain active even within the thermodynamic limit. Our results are consistent with the previous finding of disorder-free Griffiths phase that is stable at temperatures lower than the mean-field critical temperature.

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