Consider the Ising model with nearest neighbours interactions on a rectangular lattice L×M.
If L=M (2-dimensional square lattice), it is known (e.g. by Peierls argument or Onsager explicit solution) that the model exhibits a phase transition when L=M→∞.
If instead we fix L=1 (1-dimensional line) and let M→∞, the model does not exhibit a phase transition.
My question is: which relation among the side lenghts L,M guarantes the presence/absence of a phase transition? For example what about the case L=logM ?
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