  We construct a replica field theory for a random matrix model with
logarithmic confinement [K.A.Muttalib et.al., Phys. Rev. Lett. 71, 471 (1993)].
The corresponding replica partition function is calculated exactly for any size
of matrix $N$. We make a color-flavor transformation of the original model and
find corresponding Toda lattice equations for the replica partition function in
both formulations. The replica partition function in the flavor space is
defined by generalized Itzikson-Zuber (IZ) integral over homogeneous factor
space of pseudo-unitary supergroups $SU(n\mid M,M)/SU(n\mid M-N,M)$ (Stiefel
manifold) with $M\to\infty$, which is evaluated and represented in a compact
form.
