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I'm currently using the Monte Carlo Metropolis algorithm to investigate the 2D Ising model.

I have an NxN lattice of points with periodic boundary conditions imposed. I was wondering if anyone could explain why the sharpness of the phase transition is affected by the size of N?

I.e. if N is small I get a slow transition and as N is increased, the transition approaches a step function.

I don't understand why this is as I am only considering nearest neighbour interactions and by using periodic boundary conditions surely I am effectively modelling an infinite lattice? So why does the size of the unit cell affect my results?

Thanks!