The behavior of the spectrum of several quantum mechanical spin systems in the infinite volume limit.
AuthorPokorny, Martin Peter.
AdvisorKennedy, Thomas G.
MetadataShow full item record
PublisherThe University of Arizona.
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AbstractVarious results concerning the spectra of the Ising model in a strong transverse field and the anisotropic Heisenberg antiferromagnet are proved. It is proved that the ground state energy of the Ising model in a strong transverse field in all dimensions converges to its infinite volume limit exponentially with a specific power law correction. It is also proved that this model in all dimensions has continuous spectrum in the infinite volume limit. For the anisotropic Heisenberg antiferromagnet it is proved that in dimensions of at least two, the energy spectrum contains a continuous part in the infinite volume limit. All results are obtained by perturbation theory using polymer expansions.
Degree ProgramApplied Mathematics