  Monte-Carlo sampling of lattice model Hamiltonians is a well-established
technique in statistical mechanics for studying the configurational entropy of
crystalline materials. When species to be distributed on the lattice model
carry charge, the charge balance constraint on the overall system prohibits
single-site Metropolis exchanges in MC. In this article, we propose two methods
to perform MC sampling in the grand-canonical ensemble in the presence of a
charge-balance constraint. The table-exchange method (TE) constructs small
charge-conserving excitations, and the square-charge bias method (SCB) allows
the system to temporarily drift away from charge neutrality. We illustrate the
effect of internal hyper-parameters on the efficiency of these algorithms and
suggest practical strategies on how to apply these algorithms to real
applications.
