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- Title
Eigenspace Stability Conditions in Mean-Field Replica Theories.
- Authors
Landy, Jonathan
- Abstract
I consider the eigenspace form of the saddle point conditions that apply for mean-field replica models that are characterized by a single overlap matrix order parameter. These allow for a characterization of the full set of saddle point solutions. Further, they motivate consideration of a particular class of solutions, which I call the principally-commuting set. These are the solutions that simultaneously satisfy the replica-space rotational stability constraints for all physical models. I show that this set satisfies the replica equivalence symmetry, as well as other more stringent conditions, and that it also contains the set of Parisi-type ultrametric solutions as a subset.
- Subjects
SYMMETRY breaking; MEAN field models (Statistical physics); COMMUTING; STRINGENT control (Bacteria); SADDLEPOINT approximations; EIGENVALUES
- Publication
Journal of Statistical Physics, 2015, Vol 159, Issue 1, p62
- ISSN
0022-4715
- Publication type
Article
- DOI
10.1007/s10955-014-1172-y