The free energy of a two-dimensional square lattice one at low temperature is related to another one at high temperature through Kramers-Wannier duality.
Computing the partition function in the three-dimensional case with a randomly chosen interaction was shown to be NP-hard by a 1982 result of Barahona. The free energy of a two-dimensional square lattice one at low temperature is related to another one at high temperature through Kramers-Wannier duality. Bruria Kaufman used spinor analysis to compute the free energy in the one-dimensional case in 1949, simplifying her advisor's argument. It is defined on a discrete collection of spins, which can be plus or minus one, and gives a simple example of a ferromagnetic phase transition breaking a Z2 symmetry. Invented by William Lenz and given to its namesake to solve, for 10 points, what is this mathematical model of interacting spins, solved exactly in the two-dimensional case by Lars Onsager?
Computing the partition function in the three-dimensional case with a randomly chosen interaction was shown to be NP-hard by a 1982 result of Barahona.
Ising model