Computer simulations of two-dimensional melting with dipole-dipole interactions

TL;DR

This paper uses molecular dynamics and Monte Carlo simulations to study two-dimensional melting with dipole-dipole interactions, providing evidence for the hexatic phase and supporting the KTHNY theory through detailed static and dynamic analyses.

Contribution

It offers the first comprehensive simulation-based investigation of 2D melting with dipole interactions, confirming theoretical predictions and experimental observations.

Findings

Detection of algebraic decay in bond orientational correlations

Estimation of disclination unbinding temperature T_i

Extraction of critical exponents at dislocation unbinding temperature T_m

Abstract

We perform molecular dynamics and Monte Carlo simulations of two-dimensional melting with dipole-dipole interactions. Both static and dynamic behaviors are examined. In the isotropic liquid phase, the bond orientational correlation length 6 and susceptibility 6 are measured, and the data are fitted to the theoretical ansatz. An algebraic decay is detected for both spatial and temporal bond orientational correlation functions in an intermediate temperature regime, and it provides an explicit evidence for the existence of the hexatic phase. From the finite-size scaling analysis of the global bond orientational order parameter, the disclination unbinding temperature Ti is estimated. In addition, from dynamic Monte Carlo simulations of the positional order parameter, we extract the critical exponents at the dislocation unbinding temperature Tm. All the results are in agreement with those from experiments and support the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory.