Super-rough glassy phase of the random field XY model in two dimensions

Details Super-rough glassy phase of the random field XY model in two dimensions Super-rough glassy phase of the random field XY model in two dimensions

2012-04-25

arxiv.org/abs/1204.5685v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 3 figures

Scientific paper

We study both analytically, using the Renormalization Group (RG) to two loop order, and numerically, using an exact polynomial algorithm, the disorder-induced glass phase of the two-dimensional XY model with quenched random symmetry-breaking fields and without vortices. In the super-rough glassy phase, i.e. below the critical temperature T_c, the disorder and thermally averaged correlation function B(r) of the phase field \theta({\bf x}), B(r) = \bar{<[ \theta(\bf x) - \theta(\bf x+ \bf r) ]^2>} behaves, for r \gg a, as B(r) \simeq A(\tau) \, \log^2 (r/a) where r = |{\bf r}| and a is a microscopic length scale. We derive the RG equations up to cubic order in \tau = (T_c-T)/T_c and predict the universal amplitude A(\tau) = 2\tau^2-2\tau^3 + {\cal O}(\tau^4). Using an exact polynomial algorithm on an equivalent dimer version of the model we compute A(\tau) numerically and obtain a remarkable agreement with our analytical prediction, up to \tau \approx 0.5.

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