The Monte Carlo method and correlated boundary conditions

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Abstract
The authors have proposed new boundary conditions for use in Monte Carlo simulations and have applied them in this instance to the two-dimensional square Ising model. The variables defined on the first layer outside the boundary of the system are determined by the requirement that the nearest-neighbour pair correlation function with the boundary spin as one of the pair, is equal to that calculated from the finite system. The single-site values of the variables outside the boundary are chosen with a probability consistent with the fluctuations in the pair correlation function for the finite system.

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