Remark on the renormalization group equation for the Penner model.

It has been shown that it is possible to extract values for critical couplings and γstring in matrix models by deriving a renormalization group equation for the variation of the of the free energy as the size N of the matrices in the theory is varied. In this paper we derive a “renormalization group equation” for the Penner model by direct differentiation of the partition function and show that it reproduces the correct values of the critical coupling and γstring and is consistent with the logarithmic corrections present for g = 0, 1. 1 Address Sept. 1993 1994 2 Permanent Address It was observed by Brezin and Zinn-Justin [1] that the known double-scaling behaviour of the free energy F of the matrix models associated with c ≤ 1 theories F ≃ ∆0f(∆N1) (1) where ∆ = g− gc, γ0+ γ1 = 2 and γ1 = (1/12)(25− c+ √ (1− c)(25− c)) meant that they should satisfy a renormalization group equation of the form