title: Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses.
abstract: We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling distributions. All are satisfied in phases with simple thermodynamic structure, such as the droplet-scaling and chaotic pairs pictures. If instead nontrivial mixed-state pictures hold, the relations suggest that replica symmetry is broken as described by a Derrida-Ruelle cascade, with pure state weights distributed as a Poisson-Dirichlet process.
authors.affiliation: Department of Mathematics, City University of New York, Baruch College and Graduate Center, New York, New York 10010, USA.
authors.forename: L-P
authors.initials: LP
authors.lastname: Arguin
authors.affiliation: Courant Institute of Mathematical Sciences, New York, New York 10012, USA and NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China.
authors.forename: C M
authors.initials: CM
authors.lastname: Newman
authors.affiliation: Department of Physics and Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and NYU-ECNU Institutes of Physics and Mathematical Sciences at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China.
authors.forename: D L
authors.initials: DL
authors.lastname: Stein