Abstract
We have already discussed in chapter 1 the close analogy between statistical mechanics and field theory. Reinterpreting the transfer matrix as an Euclidean time evolution operator, we were led to define a corresponding quantum Hamiltonian. While in general, this will have a rather complicated form, there is a limit procedure, called the Hamiltonian limit, to simplify the structure of the transfer matrix considerably without affecting the universal properties of the critical behaviour under study [311, 129]. As compared to the isotropic transfer matrix, the resulting quantum Hamiltonian is much sparser which is useful for numerical investigations. At the same time, we also show, in the context of the Ising model, that this way the universality between different model realizations of systems in the same universality class becomes explicit in yielding the same quantum Hamiltonian. For reviews, see [227, 177].
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© 1993 Springer-Verlag Berlin Heidelberg
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(1993). The Hamiltonian Limit and Universality. In: Introduction to Conformal Invariance and Its Applications to Critical Phenomena. Lecture Notes in Physics Monographs, vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47575-0_8
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DOI: https://doi.org/10.1007/978-3-540-47575-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56504-8
Online ISBN: 978-3-540-47575-0
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