Computational Optimization of Monte-Carlo Simulation of Magnetic Ising Models

Sodium cobaltate has versatile characteristics that have been studied as potentially being used as a battery cathode, good thermoelectric material, and a superconductor when hydrated. Mobile sodium ions in Na_xCoO₂ can occupy two energetically different neighboring sites in the crystal structure. By mapping the neighboring sites onto Ising spins we are able to study the ground-state structures using Monte-Carlo simulations. In addition to general computational optimizations, various sampling methods of parameter space (i.e. uniform grid, Monte Carlo sampling and Latin Hypercube sampling) are compared to show how computational efficiency can be improved while retaining the completeness of the simulation results.