Exact Characterization ofO(n)Tricriticality in Two Dimensions

Abstract

We propose exact expressions for the conformal anomaly and for three critical exponents of the tricritical $O(n)$ loop model as a function of $n$ in the range $-2\le n\le 3/2$. These findings are based on an analogy with known relations between Potts and $O(n)$ models and on an exact solution of a “tri-tricritical” Potts model described in the literature. We verify the exact expressions for the tricritical $O(n)$ model by means of a finite-size scaling analysis based on numerical transfer-matrix calculations.