  In this work we propose a hierarchy of Monte Carlo methods for sampling
equilibrium properties of stochastic lattice systems with competing short and
long range interactions. Each Monte Carlo step is composed by two or more sub -
steps efficiently coupling coarse and microscopic state spaces. The method can
be designed to sample the exact or controlled-error approximations of the
target distribution, providing information on levels of different resolutions,
as well as at the microscopic level. In both strategies the method achieves
significant reduction of the computational cost compared to conventional Markov
Chain Monte Carlo methods. Applications in phase transition and pattern
formation problems confirm the efficiency of the proposed methods.
