Numerical simulations of a two-dimensional lattice grain boundary model

A. Jaster and H.H. Hahn

Physica A: Statistical Mechanics and its Applications, 1998, vol. 252, issue 1, 199-210

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 ξ and susceptibility χ in the high-temperature phase favour a Kosterlitz–Thouless-like (KT) singularity over a second-order phase transition. Unconstrained KT fits of χ and ξ confirm the predicted value for the critical exponent ν, while the values of η 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.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:252:y:1998:i:1:p:199-210

DOI: 10.1016/S0378-4371(97)00585-2

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