Critical behavior in some D = 1 large-N matrix models

Abstract

We study the critical behavior in D = 1 large-N matrix models with potentials of the form V(M) = ∑_kN^1-kg_ktr(M^2k) for hermitian matrices, and also those of the form V(U)= N/λ ∑_k α_k(2N-tr(U^k) - tr(U^k)) for the unitary matrices. For the planar theory, both cases show multicritical points characterized by an integer m ≥ 2 with ϒ= 2-m/2+m and ν = m-2/m+2. We also look at the subleading terms in susceptibility in order to find out the dimensions of some of the operators in the theory. The question of identification for m > 2, however, remains unsettled.