Spin-glass transition in a system with competing ferromagnetic and antiferromagnetic interaction

Abstract

Using the recently developed method of Edwards and Anderson we obtain the free energy for a system of spins interacting with an exchange potential having a distribution in the form of the sum of two Gaussians centered about $\pm J_0$ with widths $J$. When $J\ne 0$, the system undergoes a spin-glass transition only, with the ferromagnetic or antiferromagnetic phases absent. When $J=0\mathrm{}$ the system shows no transition in the molecular-field approximation used even though $J_0$ is finite. For very low temperatures and for $\frac{J}{J_0}\lesssim \frac{1}{2}$ the method gives a negative specific heat and magnetic susceptibility. These unphysical results also arose in connection with the negative entropy obtained previously for spin glasses.