Nonlinear response in the ground states of spin-glasses

A spin-glass is sensitive to an external magnetic field. An applied magnetic field dissolves degeneracy in the ground states of a spin-glass. The number of degeneracy is obtained as a function of the strength $H$ of an external magnetic field for the Edwards-Anderson model of a spinglass. Linear and nonlinear susceptibilities are studied at zero temperature. The nonlinear susceptibility ${\chi }_2$ defined by an expansion $m=\chi H+{\chi }_2{H}^3+\cdots$ for the magnetization $m$ is closely related to behavior of the local-field distribution around zero value. It is found, for the infinite-range limit of this model, that ${\chi }_2$ is a small positive quantity (0.04384) in contrast to the Sherrington-Kirkpatrick solution ($-\frac{1}{3\sqrt{2\pi }}=-0.13298\mathrm{}$). The average ground-state energy is obtained for each applied magnetic field. Comparison with computer simulations is made for the infinite-range limit.