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 D 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 M -layer construction, and it has 1 / M as the associated small parameter. Computing analytically and numerically these nonstandard diagrams at first order in the 1 / M expansion, we construct an ϵ -expansion around the upper critical dimension D uc = 8 , with ϵ = D uc − D . Following standard field theoretical methods, we can write a β function, finding a new zero-temperature fixed-point associated with the spin-glass transition in a field in dimensions D < 8 . We are also able to compute, at first order in the ϵ -expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent.