Numerical simulations of a two-dimensional lattice grain boundary model

TL;DR

This paper uses Monte Carlo simulations to analyze a 2D lattice grain boundary model, providing evidence for a Kosterlitz-Thouless transition and comparing critical exponents with the XY model.

Contribution

It offers detailed Monte Carlo analysis of a 2D grain boundary model, supporting a KT transition and exploring critical exponents and logarithmic corrections.

Findings

Evidence for KT-like transition over second-order transition

Critical exponents nu match KT predictions, eta deviate

Model likely in the same universality class as XY model

Abstract

We present detailed Monte Carlo results for a two-dimensional grain boundary model on a lattice. The effective Hamiltonian of the system results from the microscopic interaction of grains with orientations described by spins of unit length, and leads to a nearest-neighbour interaction proportional to the absolute value of the angle between the grains. Our analysis of the correlation length xi and susceptibility chi in the high-temperature phase favour a Kosterlitz-Thouless-like (KT) singularity over a second-order phase transition. Unconstrained KT fits of chi and xi confirm the predicted value for the critical exponent nu, while the values of eta deviate from the theoretical prediction. Additionally we apply finite-size scaling theory and investigate the question of multiplicative logarithmic corrections to a KT transition. As for the critical exponents our results are similar to data obtained from the XY model, so that both models probably lie in the same universality class.