Exact characterization of O(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.

arXiv commentsubmitted to Phys. Rev. Lett

References in corpus (4)

• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• Collapse of a polymer in two dimensions
• Fractal Structure of High-Temperature Graphs of O($N$) Models in Two Dimensions
• First and second order transitions in dilute O(n) models

Cited by in corpus (10)

• Conformal Random Geometry
• Cluster simulations of loop models on two-dimensional lattices
• Critical frontier for the Potts and percolation models on triangular-type and kagome-type lattices II: Numerical analysis
• Crystal lattice rules disordered states
• Ising-like transitions in the O($n$) loop model on the square lattice
• Crossover phenomena involving the dense O($n$) phase
• Tricritical O(n) models in two dimensions
• Lattice polymers with two competing collapse interactions
• Critical properties of a dilute O($n$) model on the kagome lattice
• Special transitions in an O($n$) loop model with an Ising-like constraint