%0 Book Section %1 statphys23_0537 %A Jorg, T. %A Lukic, J. %A Marinari, E. %A Martin, O.C. %A Ricci-Tersenghi, F. %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 glasses montecarlo optimization phase simulations spin statphys23 topic-9 transitions universality %T Some aspects of universality in spin glasses %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=537 %X We study universality in the spin glass (SG) transition of the two- and three-dimensional Edwards-Anderson (EA) model by means of large scale Monte Carlo (MC) simulations. We compare the finite-size scaling functions of the correlation length and the SG susceptibility for different disorder distributions. We find that our data for the three-dimensional EA model is in very good agreement with universal critical behavior. For the two-dimensional EA model, that has the SG transition at zero temperature, the analysis is more involved due to the presence of large finite-size corrections for discrete coupling distributions. A careful analysis of the data for different coupling distributions, however, reveals that also the critical behavior of the two-dimensional EA model is universal with a power-law divergence of the correlation length. This result stands in clear contrast with results from zero temperature ground state calculations where the model with bimodal couplings is supposed to have an exponential divergence while the model with Gaussian couplings is supposed to have a power-law divergence of the correlation length. This and the fact that the model with bimodal couplings has an extensive number of ground state pairs while the model with Gaussian couplings has just one pair of ground states needs further explanation. We illustrate in the framework of the Migdal-Kadanoff Renormalization Group scheme on hierarchical lattices how such a discrepancy between the properties seen at zero and at finite temperature can arise due to presence of an additional unphysical fixed point (FP) at zero temperature in the case of discrete coupling distributions. We discuss implications of this phenomenon for optimizition methods working at zero temperature and how in certain circumstances the problems related to this unphysical FP can be avoided.

@incollection{statphys23_0537, abstract = {We study universality in the spin glass (SG) transition of the two- and three-dimensional Edwards-Anderson (EA) model by means of large scale Monte Carlo (MC) simulations. We compare the finite-size scaling functions of the correlation length and the SG susceptibility for different disorder distributions. We find that our data for the three-dimensional EA model is in very good agreement with universal critical behavior. For the two-dimensional EA model, that has the SG transition at zero temperature, the analysis is more involved due to the presence of large finite-size corrections for discrete coupling distributions. A careful analysis of the data for different coupling distributions, however, reveals that also the critical behavior of the two-dimensional EA model is universal with a power-law divergence of the correlation length. This result stands in clear contrast with results from zero temperature ground state calculations where the model with bimodal couplings is supposed to have an exponential divergence while the model with Gaussian couplings is supposed to have a power-law divergence of the correlation length. This and the fact that the model with bimodal couplings has an extensive number of ground state pairs while the model with Gaussian couplings has just one pair of ground states needs further explanation. We illustrate in the framework of the Migdal-Kadanoff Renormalization Group scheme on hierarchical lattices how such a discrepancy between the properties seen at zero and at finite temperature can arise due to presence of an additional unphysical fixed point (FP) at zero temperature in the case of discrete coupling distributions. We discuss implications of this phenomenon for optimizition methods working at zero temperature and how in certain circumstances the problems related to this unphysical FP can be avoided.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Jorg, T. and Lukic, J. and Marinari, E. and Martin, O.C. and Ricci-Tersenghi, F.}, biburl = {https://www.bibsonomy.org/bibtex/2d31aa43435aa311762a54b9d441f8649/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {21e8b8df51503d2e5fe995428e1f4923}, intrahash = {d31aa43435aa311762a54b9d441f8649}, keywords = {glasses montecarlo optimization phase simulations spin statphys23 topic-9 transitions universality}, month = {9-13 July}, timestamp = {2007-06-20T10:16:22.000+0200}, title = {Some aspects of universality in spin glasses}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=537}, year = 2007 }