Following states in temperature in the spherical s+p-spin glass model

TL;DR

This paper investigates how metastable states in the spherical s+p-spin glass model evolve with temperature, revealing phenomena like level crossings, bifurcations, and limitations of the following state method at low temperatures.

Contribution

It extends previous work by analyzing state evolution in the spherical s+p-spin glass model, highlighting the effects of temperature changes and the method's limitations.

Findings

Confirmation of level crossings, bifurcations, and temperature chaos.

Identification of the limitations of the following state method at low temperatures.

Analysis of metastable state behavior near the dynamical temperature T_d.

Abstract

In many mean-field glassy systems, the low-temperature Gibbs measure is dominated by exponentially many metastable states. We analyze the evolution of the metastable states as temperature changes adiabatically in the solvable case of the spherical $s+p$-spin glass model, extending the work of Barrat, Franz and Parisi J. Phys. A 30, 5593 (1997). We confirm the presence of level crossings, bifurcations, and temperature chaos. For the states that are at equilibrium close to the so-called dynamical temperature $T_d$, we find, however, that the following state method (and the dynamical solution of the model as well) is intrinsically limited by the vanishing of solutions with non-zero overlap at low temperature.