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2D ising model explains phase transition (Para-ferro) in 3D space How?

Physics Asked on December 6, 2021

2D ising model explains phase transition (Para-ferro). How come a 2-D model explain a system where spins are distributed in all three directions?

One Answer

2D Ising model is not claimed to be the description of real ferromagnetic systems. It is a toy model, unless nontrivial, that admits an exact solution (for the case of $h = 0$) and has a phase transition.

The more realistic model, describing the real magnetism would be an $mathcal{O}(3)$ Heisenberg model in 3D. It is also an approximation to a certain extent.

Answered by spiridon_the_sun_rotator on December 6, 2021

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