Monte Carlo simulations of vacancy ordering transitions in a one-dimensional lattice gas with Coulomb interactions

Abstract

Previously, we proposed a long range mean field (LRMF) method to simplify the Hamiltonian of a one-dimensional (1D) chain with 1/ r Coulomb repulsive interactions to study the vacancy ordering transitions in quasi-1D materials such as KCu 7− x S 4. We used a self-consistent (SC) method that numerically calculated all possible solutions of average particle number distribution in the considered segment as a function of temperature. This calculation provides a possible explanation for the unusual phase transitions found in these materials. In this article, we use Monte Carlo (MC) simulations to extend our SC method. By using the MC technique we have introduced the effect of thermal fluctuations on the phase transitions in a 1D ordering system. The MC technique enables us to consider a segment of the LRMF Hamiltonian with more than 100 sites, almost an order of magnitude larger than in our previous work. The present work shows that the general results of the MC simulation are quite consistent with those of the SC method. However, the nature of the transitions and the average particle number distributions of the ground states at low temperatures are different for this model. Most importantly, the present model has thermal hysteretic behavior near phase transitions, as observed experimentally in the KCu 7− x S 4 system.