Scaling, equation of state, and the instability of the spin-glass phase

The free energy and equation of state for the Ising-type random-bond spin-glass are generated in $6-\epsilon$ dimensions with the aid of renormalization-group recursion relations. Scaling predictions based on previous renormalization-group work are borne out. The specific heat is found to be smooth with a rounded peak above the transition temperature, and the order-parameter exponent $\beta$ is greater than 1. We also find, however, that the spin-glass phase is unstable in that certain fluctuations have a negative gap. This instability leads immediately to the nonphysical prediction that the bond average of the square of a spin correlation function is negative. We conclude that there is a serious flaw in current approaches to the spin-glass phase based on the Edwards-Anderson order parameter.