Scaling Analysis of Domain-Wall Free-Energy in the Edwards-Anderson Ising Spin Glass in a Magnetic Field

TL;DR

This study investigates the stability of the spin-glass phase in three and four dimensions under a magnetic field, revealing a finite crossover length that destroys order even at infinitesimal fields, supporting droplet theory.

Contribution

It provides numerical evidence for a finite crossover length in spin glasses under magnetic fields, challenging the existence of a stable spin-glass phase in any non-zero field.

Findings

Crossover length diverges as magnetic field approaches zero.

Spin-glass order is destroyed by any non-zero magnetic field.

Results support the droplet theory for short-range spin glasses.

Abstract

The stability of the spin-glass phase against a magnetic field is studied in the three and four dimensional Edwards-Anderson Ising spin glasses. Effective couplings and effective fields associated with length scale L are measured by a numerical domain-wall renormalization group method. The results obtained by scaling analysis of the data strongly indicate the existence of a crossover length beyond which the spin-glass order is destroyed by field H. The crossover length well obeys a power law of H which diverges as H goes to zero but remains finite for any non-zero H, implying that the spin-glass phase is absent even in an infinitesimal field. These results are well consistent with the droplet theory for short-range spin glasses.