The Crisanti-Sommers Formula for Spherical Spin Glasses with Vector Spins

Abstract

We obtain the analogue of the Crisanti-Sommers variational formula for spherical spin glasses with vector spins. This formula is derived from the discrete Parisi variational formula for the limit of the free energy of constrained copies of spherical spin glasses. In vector spin models, the variations of the functional order parameters must preserve the monotonicity of matrix paths which introduces a new challenge in contrast to the derivation of the classical Crisanti-Sommers formula.

References in corpus (8)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• An Extended Variational Principle for the SK Spin-Glass Model
• On the overlap in the multiple spherical SK models
• Low Temperature Asymptotics in Spherical Mean Field Spin Glasses
• Some Properties of the Phase Diagram for Mixed $p$-Spin Glasses
• Disorder chaos in the spherical mean-field model
• Following the ground-states of full-RSB spherical spin glasses
• Free Energy of Multiple Systems of Spherical Spin Glasses with Constrained Overlaps

Cited by in corpus (4)

• Crisanti-Sommers formula and simultaneous symmetry breaking in multi-species spherical spin glasses
• Spherical Integrals of Sublinear Rank
• On properties of the spherical mixed vector p-spin model
• On ${\ell }_p$-Gaussian-Grothendieck problem