Lower lower-critical spin-glass dimension from quenched mixed-spatial-dimensional spin glasses

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 subsists 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 and shows a discontinuity to zero at d(c.)