Local excitations of a spin glass in a magnetic field

TL;DR

This study investigates the behavior of minimum energy clusters in a 3D spin glass under magnetic fields, revealing that small fields do not affect excitations and suggesting the spin glass phase is fragile against any field.

Contribution

It provides new insights into how magnetic fields influence excitations in 3D spin glasses, challenging droplet theory predictions and showing the invariance of cluster geometry.

Findings

Small fields (B<0.4) have little effect on excitations with volume V<=64.

Cluster energies decrease with volume at zero field, magnetization remains small.

All results scale as BV, indicating the spin glass phase is destroyed by any small field.

Abstract

We study the minimum energy clusters (MEC) above the ground state for the 3-d Edwards-Anderson Ising spin glass in a magnetic field. For fields B below 0.4, we find that the field has almost no effect on the excitations that we can probe, of volume V <= 64. As found previously for B=0, their energies decrease with V, and their magnetization remains very small (even slightly negative). For larger fields, both the MEC energy and magnetization grow with V, as expected in a paramagnetic phase. However, all results appear to scale as BV (instead of the B sqrt(V) expected from droplet arguments), suggesting that the spin glass phase is destroyed by any small field. Finally, the geometry of the MEC is completely insensitive to the field, giving further credence that they are lattice animals, in the presence or the absence of a field.