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Critical droplets and replica symmetry breaking

Authors :
C. M. Newman
D. L. Stein
Source :
Frontiers in Physics, Vol 12 (2024)
Publication Year :
2024
Publisher :
Frontiers Media S.A., 2024.

Abstract

We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards–Anderson–Ising model of a spin glass in arbitrary dimensions. Given a specific ground state, we suppose that the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip, leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states, as predicted by replica symmetry breaking, is equivalent to the presence of critical droplets, whose boundaries comprise a positive fraction of edges in the infinite lattice.

Details

Language :
English
ISSN :
2296424X
Volume :
12
Database :
Directory of Open Access Journals
Journal :
Frontiers in Physics
Publication Type :
Academic Journal
Accession number :
edsdoj.fd623d1edaf24fa580ad2d7569cf5e29
Document Type :
article
Full Text :
https://doi.org/10.3389/fphy.2024.1473378