Ising model, mathematical model of ferromagnetism in statistical mechanics
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She is known for contributions to Albert Einstein's theory of general relativity, to statistical physics, where she used applied spinor analysis to rederive the result of Lars Onsager on the partition function of the two-dimensional Ising Model, and to the study of the Mössbauer effect, on which she collaborated with John von Neumann and Harry Lipkin.
The DMRG has been successfully applied to get the low energy properties of spin chains: Ising model in a transverse field, Heisenberg model, etc., fermionic systems, such as the Hubbard model, problems with impurities such as the Kondo effect, boson systems, and the physics of quantum dots joined with quantum wires.
Together with Kotecký and Shlosman, he studied the formation of droplets in Ising-type models, providing mathematical justification of the Wulff construction.
For instance, the Ising model describes spins (dipoles) that have only two possible states, up and down, whereas in the Heisenberg model the spin vector is allowed to point in any direction.
Montroll had an exceptionally varied career: was a Sterling Research Fellow at Yale University where his work on the Ising model of a ferromagnet led him to solve certain Markov chain problems.