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We propose an efficient Markov Chain Monte Carlo method for sampling
equilibrium distributions for stochastic lattice models, capable of handling correctly
long and short-range particle interactions. The proposed method is a Metropolistype
algorithm with the proposal probability transition matrix based on the coarsegrained
approximating measures introduced in [17, 21]. We prove that the proposed
algorithm reduces the computational cost due to energy differences and has comparable
mixing properties with the classical microscopic Metropolis algorithm, controlled
by the level of coarsening and reconstruction procedure. The properties and
effectiveness of the algorithm are demonstrated with an exactly solvable example
of a one dimensional Ising-type model, comparing efficiency of the single spin-flip
Metropolis dynamics and the proposed coupled Metropolis algorithm.


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