A Lower Lower-Critical Spin-Glass Dimension from Quenched Mixed-Spatial-Dimensional Spin Glasses

TL;DR

This study investigates how the spin-glass phase in Ising models on hierarchical lattices vanishes at a lower-critical dimension of approximately 2.431, revealing the persistence of chaos up to the phase boundary.

Contribution

It introduces a method to study mixed-dimensional spin glasses and determines the lower-critical dimension where the spin-glass phase disappears.

Findings

Spin-glass phase vanishes at d_c=2.431.

Chaos persists up to the phase boundary.

Critical temperature approaches zero as dimension decreases.

Abstract

By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1 =< d =< 3. The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension d_c=2.431. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards d_c, the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully sustains to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring the strength of chaos, is thus largely unaffected by the approach to d_c and shows a discontinuity to zero at d_c.