Geometric effects on critical behaviours of the Ising model

TL;DR

This study explores how negative curvature in a surface influences the critical behavior of the 2D Ising model, revealing deviations from flat-plane exponents and a tendency towards mean-field values when boundary effects are minimized.

Contribution

It demonstrates that the underlying geometry of a negatively curved surface significantly alters the critical exponents of the Ising model, highlighting geometric effects on phase transition properties.

Findings

Critical exponents deviate from flat lattice values on negatively curved surfaces.

Reducing boundary effects causes exponents to approach mean-field theory predictions.

Geometry influences the critical behavior of the Ising model.

Abstract

We investigate the critical behaviour of the two-dimensional Ising model defined on a curved surface with a constant negative curvature. Finite-size scaling analysis reveals that the critical exponents for the zero-field magnetic susceptibility and the correlation length deviate from those for the Ising lattice model on a flat plane. Furthermore, when reducing the effects of boundary spins, the values of the critical exponents tend to those derived from the mean field theory. These findings evidence that the underlying geometric character is responsible for the critical properties the Ising model when the lattice is embedded on negatively curved surfaces.