%0 Book Section %1 statphys23_0660 %A Tarjus, G. %A Tissier, M. %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 critical field functional group model phenomena random renormalization statphys23 topic-2 %T Non-perturbative functional renormalization group for the random field O(N) model: the way out of dimensional reduction. %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=660 %X We have developed a non-perturbative functional renormalization group (FRG) approach for the random field O(N) model that allows us to investigate the ordering transition in any dimension d and for any value of N, including the Ising case 1. We show that the failure of dimensional reduction and of standard perturbation theory is due to the non-analytic nature of the zero-temperature fixed point controlling the critical behavior, non-analyticity which is associated with the existence of many metastable states. We find that this non-analyticity leads to critical exponents differing from the dimensional reduction prediction only below a critical dimension d*(N), with d*(N=1) near 5. The non-perturbative FRG formalism can be combined with the supersymmetric approach developed by Parisi and Sourlas for the RFIM at zero temperature2. We show that below the critical line d*(N) the supersymmetry is spontaneously broken along the RG flow. The non-perturbative FRG equations allows to properly continue the flow with a non-analytic renormalized effective action3. By means of the non-perturbative FRG, we provide a unified description of ferromagnetism, quasi-long range order and criticality in the random field O(N) model in the whole (N, d) diagram. Even though the 'dimensional reduction' property breaks down below some critical line, the topology of the phase diagram is found similar to that of the pure O(N) model, with however no equivalent of the Kosterlitz-Thouless transition. As an important output of our study, we obtain that quasi-long range order, namely a topologically ordered 'Bragg glass' phase, is absent in the 3--dimensional random field XY model4. The nonperturbative results are supplemented by a perturbative FRG analysis to two loops around d=44,5. 1) G. Tarjus and M. Tissier, Phys. Rev. Lett. 93, 267008 (2004).\\ 2) G. Parisi and N. Sourlas, Phys. Rev. Lett. 43, 744 (1979).\\ 3) M. Tissier and G. Tarjus, in preparation.\\ 4) M. Tissier and G. Tarjus, Phys. Rev. Lett. 96, 087202 (2006).\\ 5) M. Tissier and G. Tarjus, Phys. Rev. B 74, 214419 (2006).

@incollection{statphys23_0660, abstract = {We have developed a non-perturbative functional renormalization group (FRG) approach for the random field O(N) model that allows us to investigate the ordering transition in any dimension d and for any value of N, including the Ising case [1]. We show that the failure of dimensional reduction and of standard perturbation theory is due to the non-analytic nature of the zero-temperature fixed point controlling the critical behavior, non-analyticity which is associated with the existence of many metastable states. We find that this non-analyticity leads to critical exponents differing from the dimensional reduction prediction only below a critical dimension d*(N), with d*(N=1) near 5. The non-perturbative FRG formalism can be combined with the supersymmetric approach developed by Parisi and Sourlas for the RFIM at zero temperature[2]. We show that below the critical line d*(N) the supersymmetry is spontaneously broken along the RG flow. The non-perturbative FRG equations allows to properly continue the flow with a non-analytic renormalized effective action[3]. By means of the non-perturbative FRG, we provide a unified description of ferromagnetism, quasi-long range order and criticality in the random field O(N) model in the whole (N, d) diagram. Even though the 'dimensional reduction' property breaks down below some critical line, the topology of the phase diagram is found similar to that of the pure O(N) model, with however no equivalent of the Kosterlitz-Thouless transition. As an important output of our study, we obtain that quasi-long range order, namely a topologically ordered 'Bragg glass' phase, is absent in the 3--dimensional random field XY model[4]. The nonperturbative results are supplemented by a perturbative FRG analysis to two loops around d=4[4,5]. 1) G. Tarjus and M. Tissier, Phys. Rev. Lett. 93, 267008 (2004).\\ 2) G. Parisi and N. Sourlas, Phys. Rev. Lett. 43, 744 (1979).\\ 3) M. Tissier and G. Tarjus, in preparation.\\ 4) M. Tissier and G. Tarjus, Phys. Rev. Lett. 96, 087202 (2006).\\ 5) M. Tissier and G. Tarjus, Phys. Rev. B 74, 214419 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Tarjus, G. and Tissier, M.}, biburl = {https://www.bibsonomy.org/bibtex/22283c440ec09e7cec2d21671c4557ff4/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {1ed425af7ee9748f029c74fe9eda7148}, intrahash = {2283c440ec09e7cec2d21671c4557ff4}, keywords = {critical field functional group model phenomena random renormalization statphys23 topic-2}, month = {9-13 July}, timestamp = {2007-06-20T10:16:26.000+0200}, title = {Non-perturbative functional renormalization group for the random field O(N) model: the way out of dimensional reduction.}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=660}, year = 2007 }