The Ising spin glass in finite dimensions: A perturbative study of the free energy

Replica field theory is used to study the n  -dependent free energy of the Ising spin glass in a first order perturbative treatment. Large sample-to-sample deviations of the free energy from its quenched average prove to be Gaussian, independently of the special structure of the order parameter. The free energy difference between the replica symmetric and (infinite level) replica symmetry broken phases is studied in details: the line n(T)$n(T)$ where it is zero coincides with the Almeida–Thouless line for d>8$d>8$. The dimensional domain 66<d<8 is more complicated, and several scenarios are possible.