NDLI: Stable Degeneracies for Ising Models

Content Provider	Springer Nature Link
Author	Knauf, Andreas
Copyright Year	2016
Abstract	We introduce and consider the notion of stable degeneracies of translation invariant energy functions, taken at spin configurations of a finite Ising model. By this term we mean the lack of injectivity that cannot be lifted by changing the interaction.We show that besides the symmetry-induced degeneracies, related to spin flip, translation and reflection, there exist additional stable degeneracies, due to more subtle symmetries. One such symmetry is the one of the Singer group of a finite projective plane.Others are described by combinatorial relations akin to trace identities. Our results resemble traits of the length spectrum for closed geodesics on a Riemannian surface of constant negative curvature. There, stable degeneracy is defined w.r.t. Teichmüller space as parameter space.
Starting Page	551
Ending Page	571
Page Count	21
File Format	PDF
ISSN	00103616
Journal	Communications in Mathematical Physics
Volume Number	347
Issue Number	2
e-ISSN	14320916
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-02-13
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical, Mathematical and Computational Physics Mathematical Physics Quantum Physics Complex Systems Classical and Quantum Gravitation, Relativity Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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Stable Degeneracies for Ising Models