Magnetic properties of a model spin glass and the failure of linear response theory

Zero-temperature computer simulations are reported for the Sherrington-Kirkpatrick random Ising model of a spin glass, including an external field. Results are presented for the internal field distribution P(H), and for the ground state energy and magnetisation as functions of field. P(H) has a linear rise from H=0 for all external fields. The zero-temperature susceptibility chi (0) is close to unity when equilibrium states are examined, in agreement with Parisi's replica symmetry breaking theory and in conflict with linear response theory. The linear response result chi (0)=0 can be obtained by searching for metastable local energy minima close to the zero-field ground state in configuration space.