Spin-glass model of QCD near saturation

We establish a connection between the cascading of gluon momenta modeled within the diffusive approximation of the Balitsky-Fadin-Kuraev-Lipatov kernel and the thermodynamics of directed polymers on a tree with disorder. Using known results on the low-temperature spin-glass phase of this statistical mechanic problem we describe the dynamical phase space of gluon transverse momenta near saturation including its fluctuation pattern. It exhibits a nontrivial clustering structure, analogous to “hot spots”, whose distributions are derived and possess universal features in common with other spin-glass systems.