In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibriu
