Indefinitely Disordered Critical Behavior

When: Thursday, February 27, 2014 at 4:00 pm
Where: DA 5th fl
Speaker: Istvan Kovacs
Organization: University of Szeged
Sponsor: CCNR and Barabási Lab

Phase transitions are among the most striking phenomena of nature. While continuously changing a given parameter, the physical properties of the system display a sudden change at the transition point. At a continuous phase transition the emerging singularities are powerful manifestations of collective phenomena, exhibiting a broad universality: the critical behavior is insensitive to microscopic details, depending only on global characteristics. Since spatial inhomogeneity is an inevitable feature of complex systems, it is of basic importance to understand the possible effects of disorder around criticality.

In condensed matter systems the dynamics of disorder is usually slow compared to experimental time scales, thus inhomogeneities are well approximated by time-independent, quenched disorder. The main result of this field is that, quenched disorder may dramatically change the critical behavior of the system although being only a microscopic perturbation. For this scenario a paradigmatic example is the zero temperature quantum phase transition of the quantum Ising model, exhibiting an exotic, infinitely disordered critical behavior. Besides the quantum Ising model, there is a huge variety of further examples, such as the random walk in 1D or the simple infection spreading model, the contact process (SIS model). The profound effect of disorder extends also outside the critical point, in the so-called Griffiths phases, where the dynamical correlations are still long-ranged.

During the talk I give an overview about phase transitions in strongly disordered systems focusing on my results leading to the first quantitative predictions in 3 and even higher dimensional, eg. small-world networks.