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

TL;DR

This study investigates how ferromagnetic order persists on negatively curved surfaces, revealing that boundary effects sustain short-range order at high temperatures even beyond the critical point.

Contribution

It demonstrates the survival of short-range order in the Ising model on negatively curved surfaces due to boundary-spin effects, extending understanding of phase behavior in non-Euclidean geometries.

Findings

Short-range order persists at high temperatures

Boundary effects dominate ordering mechanism

Disorder-free Griffiths phase is stable below critical temperature

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.