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.
APA:
Knauf, A. (2016). Stable Degeneracies for Ising Models. Communications in Mathematical Physics, 1432-0916. https://doi.org/10.1007/s00220-016-2579-x
MLA:
Knauf, Andreas. "Stable Degeneracies for Ising Models." Communications in Mathematical Physics (2016): 1432-0916.
BibTeX: Download