Disordered criticality in two dimensions

Giancarlo Jug, B. N. Shalaev

Shanthanu Bhardwaj

Jef Hooyberghs, Ferenc Iglói, Carlo Vanderzande

The effect of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behavior is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: beta=(3-sqrt[5])/2 and nu( perpendicular )=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.

Paul Fendley, Robert Konik

The low-energy limits of models with disorder are frequently described by $\ensuremath{\sigma}$ models. In two dimensions, most $\ensuremath{\sigma}$ models admit either a Wess-Zumino-Witten term or a $\ensuremath{\theta}$ term. When such a term is present the model can have a stable critical point with gapless excitations. We describe how such a critical point appears, in particular in two-dimensional superconductors with disorder. The presence of such terms is required by the underlying (anomalous) symmetries of the original electron model. This indicates that the usual symmetry classes of disordered systems in two dimensions can be further refined. Conversely, our results also indicate that models previously thought to be in different universality classes are in fact the same once the appropriate extra terms are included.