%0 Book Section %1 statphys23_0082 %A Fedorenko, A.A. %A Doussal, P. Le %A Wiese, K.J. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K depinning disordered elastic field functional group manifolds models random renormalization statphys23 systems topic-2 transition %T A functional renormalization group approach to systems with long-range correlated disorder %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=82 %X 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.

@incollection{statphys23_0082, abstract = {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.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Fedorenko, A.A. and Doussal, P. Le and Wiese, K.J.}, biburl = {https://www.bibsonomy.org/bibtex/2b2eca16f4fe7a2bc1a16401f1c062328/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0355035ddc5df16b664c9a6a45139007}, intrahash = {b2eca16f4fe7a2bc1a16401f1c062328}, keywords = {depinning disordered elastic field functional group manifolds models random renormalization statphys23 systems topic-2 transition}, month = {9-13 July}, timestamp = {2007-06-20T10:16:11.000+0200}, title = {A functional renormalization group approach to systems with long-range correlated disorder}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=82}, year = 2007 }