Tricritical O(n) models in two dimensions

TL;DR

This paper analytically and numerically investigates the tricritical point of the two-dimensional O(n) model, providing exact universal parameters and exploring its Coulomb gas representation for n ≤ 3/2.

Contribution

It introduces an exactly solved low-temperature branch of the 2D O(n) model as a tricritical point with universal parameters, verified through transfer-matrix calculations.

Findings

Exact tricritical point for n ≤ 3/2

Universal parameters including conformal anomaly and scaling dimensions

Verification via transfer-matrix numerical methods

Abstract

We show that the exactly solved low-temperature branch of the two-dimensional O($n$) model is equivalent with an O($n$) model with vacancies and a different value of $n$. We present analytic results for several universal parameters of the latter model, which is identified as a tricritical point. These results apply to the range $n \leq 3/2$, and include the exact tricritical point, the conformal anomaly and a number of scaling dimensions, among which the thermal and magnetic exponent, the exponent associated with crossover to ordinary critical behavior, and to tricritical behavior with cubic symmetry. We describe the translation of the tricritical model in a Coulomb gas. The results are verified numerically by means of transfer-matrix calculations. We use a generalized ADE model as an intermediary, and present the expression of the one-point distribution function in that language. The analytic calculations are done both for the square and the hexagonal lattice.