1204.6221 (Zoran Ristivojevic et al.)

The super-rough phase of the Cardy-Ostlund model: two loop results    [PDF]

Zoran Ristivojevic, Pierre Le Doussal, Kay Jörg Wiese

We consider the two-dimensional XY model with quenched random symmetry-breaking fields and excluded vortices. We study the vicinity of its glass transition temperature $T_c$, in an expansion in small $\tau=(T_c-T)/T_c$ where $T$ denotes the temperature. We derive renormalization group equations in cubic order in the anharmonicity, and show that they contain two universal invariants. Using them we obtain that the correlation function in the super-rough phase for temperature $T} = \mathcal{A}\ln^2(|x|/a) + \mathcal{O}[\ln(|x|/a)]$, where the amplitude $\mathcal{A}$ is a universal function of temperature $\mathcal{A}=2\tau^2-2\tau^3+\mathcal{O}(\tau^4)$. This result differs at two-loop order, i.e. $\mathcal{O}(\tau^3)$, from the prediction based on results from the "nearly conformal" field theory of a related fermion model. We also obtain the correction-to-scaling exponent.

View original: http://arxiv.org/abs/1204.6221