Concurrent Computation and Its Application to the Study of Melting in Two Dimensions

• Main Author: Johnson, Mark Alan
• Format: Others
• Language: en
• Published: 1986
• Online Access: https://thesis.library.caltech.edu/11890/1/johnson-ma-1986.pdf; Johnson, Mark Alan (1986) Concurrent Computation and Its Application to the Study of Melting in Two Dimensions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rpeh-3z86. https://resolver.caltech.edu/CaltechTHESIS:11042019-161218997 <https://resolver.caltech.edu/CaltechTHESIS:11042019-161218997>

<p>We report an investigation of the melting transition in a two-dimensional system of particles that interact through the Lennard-Jones potential. In our investigation we attempt to determine whether the melting transition consists of a conventional first-order transition or a pair of higher-order transitions separated by a region of hexatic phase. We study systems containing 1024 and 4096 particles using Monte Carlo simulations, which we ran on Caltech’s concurrent processor. Since the concurrent Monte Carlo algorithm differs significantly from previous applications for the concurrent processor, we also explore various issues of concurrent computation. In particular, the processors must run completely asynchronously in order for the algorithm to be efficient, leading to problems satisfying detailed balance.</p> <p>We investigated the melting transition along the <i>T*</i> = .7 isotherm using constant-density simulations to measure potential energy, pressure, elastic constants, topological defects, and angular correlations. Using thermodynamic integration, we calculated the free energies of the solid and fluid phases, which we used to locate the melting transition. Both constant-density and constant-pressure simulations of the transition region confirmed the predictions of the free energy analysis. We initialized a sequence of constant-pressure simulations with a configuration from a constant-density simulation of the transition region. Using this technique, we were able to establish upper and lower bounds on the melting pressure and thereby estimate the width of the transition.</p> <p>The sharpness of the melting transition and the consistency of our various simulations give strong support to the interpretation that the melting transition is first-order. Measurements of the elastic constants and the angular correlation function provided evidence that the Kosterlitz-Thouless mechanism does not correctly describe the melting transition. Thus, we conclude that melting in the two-dimensional Lennard-Jones system at <i>T*</i> = .7 is a first-order transition. Since our simulations of the 1024-particle system exhibited strong finite-size effects in the transition region, we believe that finite-size effects dominated most previous simulations of the transition region.</p>