The large scale behavior of the simplest non-mean-field spin-glass system is analyzed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the $ϵ$-expansion technique with two independent methods. The techniques presented show how the underlying ideas of the renormalization group apply also in this disordered model, in such a way that an $ϵ$-expansion can be consistently set up. By pushing such calculation to high orders in $ϵ$, a consistent non-mean-field theory for such disordered system could be established, giving a substantial contribution the development of a predictive theory for real spin glasses.

• Received 29 June 2010

DOI:https://doi.org/10.1103/PhysRevE.82.040105