2025/02/28 by Angelini, Maria Chiara, Palazzi, Saverio, Parisi, Giorgio +1 · 1 citation
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences
paper · doi:10.48550/arxiv.2502.21089
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 ε-expansion around the upper critical dimension Duc=8, with ε=Duc-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.