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

TL;DR

This paper provides an exact analytical solution for the anisotropic special transition in the two-dimensional O(n) model, revealing critical exponents, phase diagram, and crossover behavior using advanced mathematical techniques.

Contribution

It introduces a novel exact solution for the boundary critical behavior of the 2D O(n) model with surface anisotropy, including new boundary Yang-Baxter solutions.

Findings

Full set of critical exponents derived as a function of boundary symmetry breaking

Complete phase diagram and crossover exponents obtained

New boundary Yang-Baxter solutions for loop models discovered

Abstract

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.