%0 Book Section %1 statphys23_1106 %A Lorenzo, J.J. Ruiz %A Ricci-Tersenghi, F. %A Parisi, G. %A Leuzzi, L. %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 dimensional forces glasses long off-equilibrium one phase range spin statphys23 system topic-9 transitions %T Diluted one-dimensional spin glasses with power law decaying interactions. %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1106 %X Mean-field spin glass models are known to have a rather complex low-temperature phase, which has not been clearly observed so far in numerical simulations of finite-dimensional models with short range interactions. One-dimensional spin glass models with power law decaying interactions allow to explore both regimes (long and short-range) by changing the exponent of the power law. Moreover a map can be set between the exponent value and the effective dimension of an equivalent short range interacting model. Nonetheless numerical simulations of this kind of models, where each variable interacts with all the others, are very computer demanding when increasing the system size and do not lead to any clear numerical evidence supporting a specific spin glass theory over the others. We introduce a diluted version of this model, where each variable interacts only with a finite number of others and the probability of having a link decreases as a power law with the distance of the interacting spins. The computing effort is thus substantially reduced, allowing us to simulate larger sizes for longer times. We present both the static and dynamic analysis of this model.

@incollection{statphys23_1106, abstract = {Mean-field spin glass models are known to have a rather complex low-temperature phase, which has not been clearly observed so far in numerical simulations of finite-dimensional models with short range interactions. One-dimensional spin glass models with power law decaying interactions allow to explore both regimes (long and short-range) by changing the exponent of the power law. Moreover a map can be set between the exponent value and the effective dimension of an equivalent short range interacting model. Nonetheless numerical simulations of this kind of models, where each variable interacts with all the others, are very computer demanding when increasing the system size and do not lead to any clear numerical evidence supporting a specific spin glass theory over the others. We introduce a diluted version of this model, where each variable interacts only with a finite number of others and the probability of having a link decreases as a power law with the distance of the interacting spins. The computing effort is thus substantially reduced, allowing us to simulate larger sizes for longer times. We present both the static and dynamic analysis of this model.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lorenzo, J.J. Ruiz and Ricci-Tersenghi, F. and Parisi, G. and Leuzzi, L.}, biburl = {https://www.bibsonomy.org/bibtex/2efb4e67e0fe017d48df16b36ac05c477/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {fc972a6ca3ac8b0d47c5be78b051743b}, intrahash = {efb4e67e0fe017d48df16b36ac05c477}, keywords = {dimensional forces glasses long off-equilibrium one phase range spin statphys23 system topic-9 transitions}, month = {9-13 July}, timestamp = {2007-06-20T10:16:39.000+0200}, title = {Diluted one-dimensional spin glasses with power law decaying interactions.}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=1106}, year = 2007 }