Critical exponents of the spin-glass transition in a field at zero temperature.

Abstract

We analyze the spin-glass transition in a field in finite dimension [Formula: see text] below the upper critical dimension directly at zero temperature using a recently introduced perturbative loop expansion around the Bethe lattice solution. The expansion is generated by the so-called [Formula: see text]-layer construction, and it has [Formula: see text] as the associated small parameter. Computing analytically and numerically these nonstandard diagrams at first order in the [Formula: see text] expansion, we construct an [Formula: see text]-expansion around the upper critical dimension [Formula: see text], with [Formula: see text]. Following standard field theoretical methods, we can write a [Formula: see text] function, finding a new zero-temperature fixed-point associated with the spin-glass transition in a field in dimensions [Formula: see text]. We are also able to compute, at first order in the [Formula: see text]-expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent.