Chaotic Nature of the Spin-Glass Phase

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