One-step replica-symmetry-breaking phase in low-dimensional spin glasses

It is long known that mean-field theory of an Ising spin glass predicts a second-order phase boundary in the temperature–magnetic field plane between a paramagnet and a replica-symmetry-breaking phase. Here, we show that at nonzero magnetic fields and just above six dimensions, this phase diagram is modified by the appearance of a one-step replica symmetry-breaking phase below the transition, and a tricritical point beyond which the transition becomes quasi-first-order. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in less-than-six-dimensional spin glasses in simulations and high-temperature series expansions.