Discreteness and entropic fluctuations in GREM-like systems

TL;DR

This paper investigates how energy discreteness and entropy affect the behavior of GREM-like systems at low temperatures, revealing effects on replica symmetry breaking and overlap distributions.

Contribution

It demonstrates that energy discreteness induces replica symmetry breaking at zero temperature, but extensive entropy can smooth out differences in overlap distributions across phases.

Findings

Discreteness causes replica symmetry breaking at zero temperature.

Extensive entropy leads to a delta function in overlap distribution.

Entropy fluctuations smooth out differences between discrete and continuous models.

Abstract

Within generalized random energy models, we study the effects of energy discreteness and of entropy extensivity in the low temperature phase. At zero temperature, discreteness of the energy induces replica symmetry breaking, in contrast to the continuous case where the ground state is unique. However, when the ground state energy has an extensive entropy, the distribution of overlaps P(q) instead tends towards a single delta function in the large volume limit. Considering now the whole frozen phase, we find that P(q) varies continuously with temperature, and that state-to-state fluctuations of entropy wash out the differences between the discrete and continuous energy models.