Exact solution of the anisotropic special transition in the O(n) model in 2D

Details Exact solution of the anisotropic special transition in the O(n) model in 2D Exact solution of the anisotropic special transition in the O(n) model in 2D

2009-09-16

arxiv.org/abs/0909.2949v1

Physical Review Letters 103 (2009) 145701

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.103.145701

The effect of surface exchange anisotropies is known to play a important role in magnetic critical and multicritical behavior at surfaces. We give an exact analysis of this problem in d=2 for the O(n) model by using Coulomb gas, conformal invariance and integrability techniques. We obtain the full set of critical exponents at the anisotropic special transition--where the symmetry on the boundary is broken down to O(n_1)xO(n-n_1)--as a function of n_1. We also obtain the full phase diagram and crossover exponents. Crucial in this analysis is a new solution of the boundary Yang-Baxter equations for loop models. The appearance of the generalization of Schramm-Loewner Evolution SLE_{\kappa,\rho} is also discussed.

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