The perturbative approach to the critical behaviour of two-matrix models in the limit N → ∞ Original Research Article

We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators B1,2 tend to differential operators of order l2,1, respectively, the singularity is characterized by (l1, l2). Let l1 ⩾ l2. Then the two cases, (A) “l2 does not divide l1” and (B) “l2 divides l1”, need a different treatment. The universality classes are labelled [p, q] where [p, q] = [l1,l2] in case (A) and [p, q]=[l1 + 1,l2] in case (B).