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It's expected that the pressure of the Ising model on da $d$-dimensional discrete torus with side length L$L$ converges to the means fieldmean-field Ising model pressure as the dimension d$d$ goes to infinity. Is there a rigorous proof for this fact intuitively? Intuitively this is indeed true. thanksThanks for any references.

It's expected that the pressure of Ising model on d-dimensional discrete torus with side length L converges to the means field Ising model pressure as the dimension d goes to infinity. Is there a rigorous proof for this fact intuitively this is indeed true. thanks for any references.

It's expected that the pressure of the Ising model on a $d$-dimensional discrete torus with side length $L$ converges to the mean-field Ising model pressure as the dimension $d$ goes to infinity. Is there a rigorous proof for this fact? Intuitively this is indeed true. Thanks for any references.

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Ising model on torus

It's expected that the pressure of Ising model on d-dimensional discrete torus with side length L converges to the means field Ising model pressure as the dimension d goes to infinity. Is there a rigorous proof for this fact intuitively this is indeed true. thanks for any references.