Temperature dependence in random matrix models with pairing condensates

We address a number of issues raised by a manuscript of Klein, Toublan, and Verbaarschot [hep-ph/0405180] in which the authors introduce a random matrix model for QCD with two colors, two flavors, and fermions in the fundamental representation. Their inclusion of temperature terms differs from the approach adopted in previous work on this problem [Phys. Rev. D 64, 074016 (2001)]. We demonstrate that the two approaches are related by a transformation that leaves the thermodynamic potential invariant and which therefore has no effect on physical observables.