Discontinuous molecular dynamics simulations in an external field: Application to two-dimensional ferrofluids.

We introduce a stochastic method for simulating the effect of an external magnetic field on coarse-grained models of magnetic colloids for use in discontinuous molecular dynamics (DMD) simulations. Our method for simulating an external field is illustrated with a coarse-grained model for magnetic squares in two dimensions. Square-shaped particles are represented as four disks bonded together in a 2×2 lattice configuration to create a hard colloidal geometry. Two opposite charges are embedded within the square to mimic the magnetic interactions between particles. The method for simulating an external field stochastically during DMD simulations operates by applying impulses randomly to the charges embedded within each square particle. When one square experiences an interaction with the field, each embedded charge within the square is assigned a new momentum with a specific magnitude and orientation. The magnitude of this momentum is equal to the average of a Maxwell-Boltzmann distribution at the simulation temperature. The orientation of the momentum depends on the charge, either positive or negative, and points either in the same or opposite direction as the field, respectively. The strength of the external field is determined by the average frequency at which the particles experience interactions with the field. The relationship between the stochastic frequency of the field and the field strength is derived from Newton's equation of motion. DMD simulations are performed for large systems of magnetic square particles at various temperatures and external field strengths. The simulation temperature is maintained constant with an Andersen thermostat, while the external field is simulated stochastically, as described above. We find that our simulation techniques reproduce a net system magnetization in close agreement with the two-dimensional equivalent of the Langevin function, while maintaining the simulation temperature constant.