Zusammenfassung
Functional Renormalization group (FRG) is a promising new method,
which can handle disordered systems even when other methods fail
due to glassy behavior, existence of multiple minima, ``dimensional reduction'',
etc. Most FRG studies are restricted to uncorrelated point-like disorder, however, real systems often contain extended defects in the form of linear dislocations, planar grain boundaries, three-dimensional cavities, etc. We generalized FRG to study systems with long-range correlated disorder.
We studied the statics and dynamics of elastic manifolds in disordered
media with long-range correlated disorder Phys. Rev. E 74, 061109 (2006).
We identified different universality classes and computed the critical exponents and universal amplitudes describing geometric and velocity-force characteristics. In contrast to uncorrelated disorder, at depinning a velocity-versus-force exponent can be larger than unity as is usually observed in experiments. The statistical tilt symmetry is broken resulting in a
nontrivial response to a transverse tilting force. For instance, the vortex lattice in disordered superconductors shows a new glass phase whose properties interpolate between those of the Bragg and Bose glasses formed by point-like and columnar disorder, respectively. Whereas there is no response in the Bose glass phase (transverse Meissner effect), the standard linear response expected in the Bragg glass gets modified to a power law response in the presence of disorder correlations. We studied the long distance properties of the $O(N)$ spin system with random fields and random anisotropies correlated as $1/x^d-\sigma$ cond-mat/0701256. Using FRG we obtained the phase diagram in $(d,\,\sigma,\,N)$-parameter space and computed the corresponding critical exponents. We found that below the lower critical dimension $4+\sigma$, there can exist two different types of quasi-long-range-order with zero order-parameter but infinite correlation length. The existence of two different
phases of 3He-A in aerogel which can be described by our model has been recently
observed in experiments.
Links und Ressourcen
Tags