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 exa
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