Monte Carlo studies of a Laplacian roughening model for two-dimensional melting

Abstract

Monte Carlo simulations are used to study the thermodynamic properties of the Laplacian roughening model. Nelson has shown that this model is related via a duality transformation to a gas of disclinations in a two-dimensional solid, and mimics the positional and orientational symmetries relevant to two-dimensional melting. In our simulations thermodynamic functions vary continuously over the full temperature range and agree with analytic results at low and high temperatures. Correlation functions exhibit three distinct regimes as a function of temperature and yield strong evidence for the existence of an intermediate phase characterized by short-range positional order and quasi-long-range orientational order. The Monte Carlo results are in quantitative agreement with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory and establish the existence of two successive continuous phase transitions for the Laplacian roughening model. The corresponding transition temperatures are obtained from the temperature dependence of the renormalized elastic constant ${K}_{R}$ and the Frank constant ${K}_{A}$.