Simulation calculation of dielectric constants: Comparison of methods on an exactly solvable model

Abstract

A mean spherical model of classical dipoles on a simple cubic lattice of sideM=2N+1 sites is considered. Exact results are obtained for finite systems using periodic boundary conditions with an external dielectric constantɛ′ and using reaction field boundary conditions with a cutoff radiusRc⩽N and an external dielectric constantɛ′. The dielectric constant in the disordered phase is calculated using a variety of fluctuation formulas commonly implemented in Monte Carlo and molecular dynamics simulations of dipolar systems. The coupling in the system is measured by the parametery=4πμ2/9kT, whereμ2 is the fixed mean square value of the dipole moments on the lattice. The system undergoes a phase transition aty≈2.8, so that very high dielectric constants cannot be obtained in the disordered phase. The results show clearly the effects of system size, cutoff radius, external dielectric constant, and different measuring techniques on a dielectric constant estimate. It is concluded that with periodic boundary conditions, the rate of approach of the dielectric constant estimate to its thermodynamic limit is asN−2/3 and depends only weakly onɛ′. Methods of implementing reaction field boundary conditions to give rapid convergence to the thermodynamic limit are discussed.