Tricritical O(n) models in two dimensions

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 $n\le 3/2$, 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.

24 pages, 4 figures

References in corpus (6)

• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Cluster simulations of loop models on two-dimensional lattices
• Applications of Temperley-Lieb algebras to Lorentz lattice gases
• Fractal Structure of High-Temperature Graphs of O($N$) Models in Two Dimensions
• Exact characterization of O(n) tricriticality in two dimensions

Cited by in corpus (5)

• Ising-like transitions in the O($n$) loop model on the square lattice
• Crossover phenomena involving the dense O($n$) phase
• Lattice polymers with two competing collapse interactions
• Crossing bonds in the random-cluster model
• Renormalization of crossing probabilities in the dilute Potts model