Chaotic Nature of the Spin-Glass Phase

Abstract

The description of the spin-glass phase in terms of a $T=0$ fixed point is shown to imply a "chaotic" phase in which the relative orientations of spins with large separations $L\ensuremath{\gtrsim}{L}^{*}$ are sensitive to small changes $\ensuremath{\delta}T$ in the temperature or $\ensuremath{\delta}J$ in the bond strengths, where ${L}^{*}\ensuremath{\propto}\frac{1}{{(\ensuremath{\delta}T)}^{\frac{1}{\ensuremath{\zeta}}}}$ or $\frac{1}{{(\ensuremath{\delta}J)}^{\frac{1}{\ensuremath{\zeta}}}}$, respectively, $\ensuremath{\zeta}=\frac{{d}_{s}}{2\ensuremath{-}y}$, and $\ensuremath{-}y$ and ${d}_{S}$ are the thermal eigenvalue at the $T=0$ fixed point and the "interfacial (fractal) dimension," respectively.