%0 Book Section %1 statphys23_0713 %A Hukushima, K. %A Campbell, I.A. %A Takayama, H. %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 exponent glass phenomena scaling spin statphys23 topic-9 %T Extended scaling scheme and its application to spin glasses %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=713 %X Critical phenomena of continuous phase transitions is one of the most sophisticated topics in the field of statistical mechanics. Critical divergences of thermodynamic quantities at a transition temperature $T_c$ are conventionally expressed as a power law in terms of a scaling variable $T-T_c$. It has been emphasized that the critical power-law expression is valid only in the immediate vicinity of $T_c$, which is a very restrictive condition both for numerical simulations and experiments. In particular, it is difficult to analyze finite size numerical data of spin-glass models while complying strictly with this condition. In fact, a naive finite-size-scaling analysis in early studies of three-dimensional Ising spin glasses lead to inconsistent estimates for the critical exponent $\nu$ obtained from different observables. Recently, we proposed an extended scaling scheme1,2 for critical phenomena of continuous phase transitions, which is based on the intrinsic structure of high-temperature series expansions. The extended scaling expressions are systematically derived for thermodynamic observables in ferromagnets and in spin glasses. These provide good leading-order critical representations for a wide range of temperature, which is significantly enlarged as compared with the conventional scaling scheme. With appropriate choices of scaling variables and non-critical prefactors, in both ferromagnets and spin glasses the leading critical term provides a good approximation to the true behavior of susceptibility and correlation length from $T_c$ up to infinite temperature. The expressions should be of practical importance for estimating critical exponents in spin glasses, when the data available from numerical simulations as well as experiments are typically at temperatures higher than $T_c$ by more than ten percent. Using the extended scaling scheme, we obtain a consistent set of critical exponents of the three-dimensional Ising spin glass with bimodal distribution from finite-size scalings for different observables, in contrast to previous studies by the conventional scaling. We also report an application of our scheme to treat the correction terms for some canonical ferromagnets. 1) I.A.Camplbell, K. Hukushima and H.Takayama, Phys.Rev.Lett. 97, 117202(2006)\\ 2) I.A.Camplbell, K. Hukushima and H.Takayama, cond-mat/0612665.

@incollection{statphys23_0713, abstract = {Critical phenomena of continuous phase transitions is one of the most sophisticated topics in the field of statistical mechanics. Critical divergences of thermodynamic quantities at a transition temperature $T_c$ are conventionally expressed as a power law in terms of a scaling variable $T-T_c$. It has been emphasized that the critical power-law expression is valid only in the immediate vicinity of $T_c$, which is a very restrictive condition both for numerical simulations and experiments. In particular, it is difficult to analyze finite size numerical data of spin-glass models while complying strictly with this condition. In fact, a naive finite-size-scaling analysis in early studies of three-dimensional Ising spin glasses lead to inconsistent estimates for the critical exponent $\nu$ obtained from different observables. Recently, we proposed an extended scaling scheme[1,2] for critical phenomena of continuous phase transitions, which is based on the intrinsic structure of high-temperature series expansions. The extended scaling expressions are systematically derived for thermodynamic observables in ferromagnets and in spin glasses. These provide good leading-order critical representations for a wide range of temperature, which is significantly enlarged as compared with the conventional scaling scheme. With appropriate choices of scaling variables and non-critical prefactors, in both ferromagnets and spin glasses the leading critical term provides a good approximation to the true behavior of susceptibility and correlation length from $T_c$ up to infinite temperature. The expressions should be of practical importance for estimating critical exponents in spin glasses, when the data available from numerical simulations as well as experiments are typically at temperatures higher than $T_c$ by more than ten percent. Using the extended scaling scheme, we obtain a consistent set of critical exponents of the three-dimensional Ising spin glass with bimodal distribution from finite-size scalings for different observables, in contrast to previous studies by the conventional scaling. We also report an application of our scheme to treat the correction terms for some canonical ferromagnets. 1) I.A.Camplbell, K. Hukushima and H.Takayama, Phys.Rev.Lett. 97, 117202(2006)\\ 2) I.A.Camplbell, K. Hukushima and H.Takayama, cond-mat/0612665.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Hukushima, K. and Campbell, I.A. and Takayama, H.}, biburl = {https://www.bibsonomy.org/bibtex/23b933df29a0b55eec3e1933b83d18105/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {dfb4136d4a1c1682309fe1b754c12c27}, intrahash = {3b933df29a0b55eec3e1933b83d18105}, keywords = {critical exponent glass phenomena scaling spin statphys23 topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:27.000+0200}, title = {Extended scaling scheme and its application to spin glasses}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=713}, year = 2007 }