Multicritical two-dimensional vertex models

Abstract

We study the multicritical behavior of a class of two-dimensional ice-type vertex models on different lattices using renormalization-group theory. The models are classified by an integer m, with m=2 corresponding to the known square lattice case. For m>2, the specific-heat exponent is a=(m-2)/(m-1) with an upper critical dimensional confluent (lnt)^1/2 divergence for m=3. The nature of the transition is similar to the mth-order multicritical point, yet the exponents are not those known from c<1 conformal invariance. The models are anisotropic with v_||=1 and v_⊥=12. A few special features of the models are discussed.