Correct initialization and update method of the local simulation for electrostatic interactions

The local simulation algorithm for the electrostatic interactions, proposed by Maggs and Rossetto, serves as a fast simulation technique to consider electrolytes. The algorithm draws upon the auxiliary field variables on the lattice and may involve two topologically disconnected update schemes: the closed-loop and straight-line plaquette updates. We show that the straight-line update leads to unphysical configurations because the electrostatic field and system energy tend to diverge as the system size approaches zero. Such an unphysical state can be quickly decoupled from the observables by combining the closed-loop and straight-line updates. Alternatively, the simulation without the straight-line update becomes accurate when the initial configuration of the auxiliary field variables does not form the string-like structure on the lattice. We thus discuss an appropriate initial condition and an update method.