Sheared Ising models in three dimensions

TL;DR

This study investigates nonequilibrium phase transitions in sheared three-dimensional Ising models using Monte Carlo simulations, revealing anisotropic critical behavior and exact correlation function forms under high shear conditions.

Contribution

It provides the first detailed analysis of anisotropic phase transitions in sheared 3D Ising models, including critical exponents and exact correlation functions.

Findings

Critical temperature depends on shear direction

Anisotropy exponent theta=2, nu_parallel=1, nu_perp=1/2

Correlation functions perpendicular to shear are Ornstein-Zernike

Abstract

The nonequilibrium phase transition in sheared three-dimensional Ising models is investigated using Monte Carlo simulations in two different geometries corresponding to different shear normals. We demonstrate that in the high shear limit both systems undergo a strongly anisotropic phase transition at exactly known critical temperatures T_c which depend on the direction of the shear normal. Using dimensional analysis, we determine the anisotropy exponent theta=2 as well as the correlation length exponents nu_parallel=1 and nu_perp=1/2. These results are verified by simulations, though considerable corrections to scaling are found. The correlation functions perpendicular to the shear direction can be calculated exactly and show Ornstein-Zernike behavior.