The SK model is infinite step replica symmetry breaking at zero temperature

Abstract

We prove that the Parisi measure of the mixed p-spin model at zero temperature has infinitely many points in its support. This establishes Parisi's prediction that the functional order parameter of the Sherrington-Kirkpatrick model is not a step function at zero temperature. As a consequence, we show that the number of levels of broken replica symmetry in the Parisi formula of the free energy diverges as the temperature goes to zero.

revised version; 20 pages

References in corpus (3)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Low Temperature Asymptotics in Spherical Mean Field Spin Glasses
• Double Criticality of the Sherrington-Kirkpatrick Model at T=0

Cited by in corpus (1)

• Missing Puzzle Pieces in the Performance Landscape of the Quantum Approximate Optimization Algorithm