%0 Book Section %1 statphys23_0226 %A Oppermann, R. %A Schmidt, M.J. %A Sherrington, D. %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 criticality dimensional effective field glass one-dimensional order rsb-related scaling shift spaces spin statphys23 theory topic-9 %T Critical behaviour and scaling of the SK-model in the low T limit: numerical analysis and analytic modeling of frustrated order %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=226 %X Solutions up to very high orders of replica symmetry breaking of a selfconsistent T=0 scheme are used to identify critical behaviour and scaling in the low T limit of the SK-model 1,2. Results on a lattice of 100 'sites' of different RSB-orders, as obtained by means of a new numerico-analytical technique3, suffice to control 'length'-scaling towards the RSB-continuum limit. The new technique also produces results for finite temperatures, incl. the complete low T crossover (and finite fields too). A scaling theory based on the precise data is proposed. Analytic modeling of the T=0 order function q(a) is given by a confluent hypergeometric function (without break point at T=0), which unfolds the nontrivial q-distribution of the Parisi function q(x,T=0) at x=0 1,2. The new variable a=x/T is interpreted as an inverse pseudo-time. Two critical points arise at a=0 and at $a=ınfty$. Introduction of a new order function leads to a pseudo-time relaxational (Langevin-type) differential equation, which is supposed to serve as a step towards a new effective field theory of spin glasses 1. The existence of discrete spectra of Parisi block size ratios are resolved with high accuracy in the short- and long-pseudotime limits 1 of the continuum RSB limit at T=0 and H=0. Various observations such as mysterious Coulomb-analogies, a kink-like shape of the order function on logarithmic scale, and symmetries of data and their analytical (approximate) representation are presented. A variety of field theoretical models will be discussed, which can be linked or reduced to the SK-model. In particular Halperin-Hohenberg type models and their renormalization are considered. 1 R. Oppermann, M.J. Schmidt, D. Sherrington, Phys.Rev.Lett.98,127201(2007) 2 R. Oppermann, D. Sherrington, Phys.Rev.Lett. 95, 197203 (2005) 3 M.J. Schmidt, R. Oppermann, W$u$rzburg-preprint (2007)

@incollection{statphys23_0226, abstract = {Solutions up to very high orders of replica symmetry breaking of a selfconsistent T=0 scheme are used to identify critical behaviour and scaling in the low T limit of the SK-model [1,2]. Results on a lattice of 100 'sites' of different RSB-orders, as obtained by means of a new numerico-analytical technique[3], suffice to control 'length'-scaling towards the RSB-continuum limit. The new technique also produces results for finite temperatures, incl. the complete low T crossover (and finite fields too). A scaling theory based on the precise data is proposed. Analytic modeling of the T=0 order function q(a) is given by a confluent hypergeometric function (without break point at T=0), which unfolds the nontrivial q-distribution of the Parisi function q(x,T=0) at x=0 [1,2]. The new variable a=x/T is interpreted as an inverse pseudo-time. Two critical points arise at a=0 and at $a=\infty$. Introduction of a new order function leads to a pseudo-time relaxational (Langevin-type) differential equation, which is supposed to serve as a step towards a new effective field theory of spin glasses [1]. The existence of discrete spectra of Parisi block size ratios are resolved with high accuracy in the short- and long-pseudotime limits [1] of the continuum RSB limit at T=0 and H=0. Various observations such as mysterious Coulomb-analogies, a kink-like shape of the order function on logarithmic scale, and symmetries of data and their analytical (approximate) representation are presented. A variety of field theoretical models will be discussed, which can be linked or reduced to the SK-model. In particular Halperin-Hohenberg type models and their renormalization are considered. [1] R. Oppermann, M.J. Schmidt, D. Sherrington, Phys.Rev.Lett.98,127201(2007) [2] R. Oppermann, D. Sherrington, Phys.Rev.Lett. 95, 197203 (2005) [3] M.J. Schmidt, R. Oppermann, W$\ddot{u}$rzburg-preprint (2007)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Oppermann, R. and Schmidt, M.J. and Sherrington, D.}, biburl = {https://www.bibsonomy.org/bibtex/2d1310273d1efbf553ca6e9cd670970f7/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {8a6dc508aef4d2a5e78d8dcbd8d07c8a}, intrahash = {d1310273d1efbf553ca6e9cd670970f7}, keywords = {criticality dimensional effective field glass one-dimensional order rsb-related scaling shift spaces spin statphys23 theory topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:14.000+0200}, title = {Critical behaviour and scaling of the SK-model in the low T limit: numerical analysis and analytic modeling of frustrated order}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=226}, year = 2007 }