Driven and Non-Driven Surface Chaos in Spin-Glass Sponges

TL;DR

This study uses renormalization-group theory to analyze surface and bulk spin-glass ordering in three-dimensional systems with smooth or fractal surfaces, revealing complex phase diagrams and chaotic behaviors.

Contribution

It introduces a detailed phase diagram for spin-glass systems with fractal surfaces, highlighting surface-only ordering and multicritical points.

Findings

Surface does not order without bulk in smooth surfaces.

Fractal surfaces can have surface ordering without bulk ordering.

Distinct chaotic trajectories characterize different spin-glass phases.

Abstract

A spin-glass system with a smooth or fractal outer surface is studied by renormalization-group theory, in bulk spatial dimension d=3. Independently varying the surface and bulk random-interaction strengths, phase diagrams are calculated. The smooth surface does not have spin-glass ordering in the absence of bulk spin-glass ordering and always has spin-glass ordering when the bulk is spin-glass ordered. With fractal (d>2) surfaces, a sponge is obtained and has surface spin-glass ordering also in the absence of bulk spin-glass ordering. The phase diagram has the only-surface-spin-glass ordered phase, the bulk and surface spin-glass ordered phase, and the disordered phase, and a special multicritical point where these three phases meet. All spin-glass phases have distinct chaotic renormalization-group trajectories, with distinct Lyapunov and runaway exponents which we have calculated.