Tricritical O(n) models in two dimensions

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 78; no. 6 Pt 1; p. 061104
• Main Authors: Nienhuis, Bernard, Guo, Wenan, Blöte, Henk W J
• Format: Journal Article
• Language: English
• Published: United States 01.12.2008
• ISSN: 1539-3755
• DOI: 10.1103/PhysRevE.78.061104

We show that the exactly solved low-temperature branch of the two-dimensional O(n) model is equivalent to 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</=32 and include the exact tricritical point, the conformal anomaly, and a number of scaling dimensions, among which are the thermal and magnetic exponents, and the exponent associated with the 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 honeycomb lattice.