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 non-standard diagrams at first order in the $1/M$ expansion, we construct an $\hat{I}\mu$-expansion around the upper critical dimension $D_{\text{uc}}=8$, with $\hat{I}\mu =D_{\text{uc}}-D$. Following standard field theoretical methods, we can write a ${\hat{I}}^2$ 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 $\hat{I}\mu$-expansion, the three independent critical exponents characterizing the transition, plus the correction-to-scaling exponent.

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