Exact characterization of O(n) tricriticality in two dimensions

TL;DR

This paper derives exact formulas for critical properties of the two-dimensional tricritical O(n) loop model across a range of n, verified through numerical analysis, advancing understanding of phase transitions in statistical physics.

Contribution

It provides the first exact expressions for the conformal anomaly and critical exponents of the tricritical O(n) model as functions of n, based on an analogy with Potts models and an exact solution.

Findings

Exact expressions for conformal anomaly and critical exponents as functions of n.

Verification of formulas through finite-size scaling and transfer-matrix calculations.

Extension of known relations between Potts and O(n) models to tricritical points.

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 $-2 \leq n \leq 3/2$. 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.