Entropic long range order in a 3D spin glass model

TL;DR

This paper reveals a new form of entropic long-range order in a 3D spin glass model, showing that spins can be correlated over long distances purely due to entropy, even without energy stiffness.

Contribution

It demonstrates the existence of entropic long-range order in a 3D spin glass model at zero temperature and low link density, a novel phenomenon not previously identified.

Findings

Long-range spin correlations exist without energy stiffness.

Entropic effects induce order at zero temperature.

Phase diagram region with entropic long-range order identified.

Abstract

We uncover a new kind of entropic long range order in finite dimensional spin glasses. We study the link-diluted version of the Edwards-Anderson spin glass model with bimodal couplings (J=+/-1) on a 3D lattice. By using exact reduction algorithms, we prove that there exists a region of the phase diagram (at zero temperature and link density low enough), where spins are long range correlated, even if the ground states energy stiffness is null. In other words, in this region twisting the boundary conditions cost no energy, but spins are long range correlated by means of pure entropic effects.