Stable Degeneracies for Ising Models

Knauf A (2016)

Publication Type: Journal article, Original article

Publication year: 2016


Publisher: Springer Verlag (Germany)

Pages Range: 1432-0916

DOI: 10.1007/s00220-016-2579-x


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.

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How to cite


Knauf, A. (2016). Stable Degeneracies for Ising Models. Communications in Mathematical Physics, 1432-0916.


Knauf, Andreas. "Stable Degeneracies for Ising Models." Communications in Mathematical Physics (2016): 1432-0916.

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