  We consider the $\pm J$ Ising model on a cubic lattice with a gauge-invariant
disorder distribution. Disorder depends on a parameter $\beta_G$ that plays the
role of a chemical potential for the amount of frustration. We study the model
at a specific value of the disorder parameter $\beta_G$, where frustration
shows long-range correlations. We characterize the universality class,
obtaining accurate estimates of the critical exponents: $\nu = 0.655(15)$ and
$\eta_q = 1.05(5)$, where $\eta_q$ is the overlap susceptibility exponent.
