%0 Book Section %1 statphys23_0592 %A Ozeki, Y. %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 disordered fixed gauge glass ising j method model nonequilibrium point random relaxation statphys23 systems topic-9 %T Nonequilibrium Relaxation Studies for Universality Classes and Random Fixed Point in Some Disordered Systems %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=592 %X The universality classes and the possibility of random fixed point are studied for some disordered systems. The $J$ Ising model in 2D and 3D, the $XY$ gauge glass model in 3D, and the $Z_q$ random $XY$ model in 2D and 3D are investigated. The nonequilibrium relaxation (NER) method together with the analysis of fluctuations is applied to estimate the transition temperature and critical exponents. We have found the existence of the random fixed point for the 3D $J$ Ising model and the absence of it for the 2D case 1. Due to the Harris criterion 2, the existence of the random fixed point depends on the sign of the specific heat exponent $\alpha$ in non-random case. It has been known that $\alpha>0$ for the 3D FM Ising model and $\alpha=0$ for the 2D FM one (the logarithmic divergence; the marginal case). The present observation is consistent with the Harris criterion. The same analysis is applied to the $XY$ system in 3D, where the randomness is assigned as the gauge glass type. In this model, we also examine the university for the SG transition along the PM-SG phase boundary. We also investigate the $Z_q$ random $XY$ model. In 3D, the universality class at the multicritical point for finite values of $q$, is the same as the continuous $XY$ case, which is a similar behavior with the non-random case. In 2D, using the NER scaling analysis for the KT transition, we estimate the transition temperatures of PM-KT-FM transitions for several values of $q$, and find the agreement with the hypothesis from the duality theory3. 1) Y. Ozeki and N. Ito, submitted to J. Phys. A\\ 2) A. B. Harris, J. Phys. C7 (1974) 1671\\ 3) K. Takeda, T. Sasamoto and H. Nishimori, J. Phys. A38 (2005) 3751.

@incollection{statphys23_0592, abstract = {The universality classes and the possibility of random fixed point are studied for some disordered systems. The $\pm J$ Ising model in 2D and 3D, the $XY$ gauge glass model in 3D, and the $Z_q$ random $XY$ model in 2D and 3D are investigated. The nonequilibrium relaxation (NER) method together with the analysis of fluctuations is applied to estimate the transition temperature and critical exponents. We have found the existence of the random fixed point for the 3D $\pm J$ Ising model and the absence of it for the 2D case [1]. Due to the Harris criterion [2], the existence of the random fixed point depends on the sign of the specific heat exponent $\alpha$ in non-random case. It has been known that $\alpha>0$ for the 3D FM Ising model and $\alpha=0$ for the 2D FM one (the logarithmic divergence; the marginal case). The present observation is consistent with the Harris criterion. The same analysis is applied to the $XY$ system in 3D, where the randomness is assigned as the gauge glass type. In this model, we also examine the university for the SG transition along the PM-SG phase boundary. We also investigate the $Z_q$ random $XY$ model. In 3D, the universality class at the multicritical point for finite values of $q$, is the same as the continuous $XY$ case, which is a similar behavior with the non-random case. In 2D, using the NER scaling analysis for the KT transition, we estimate the transition temperatures of PM-KT-FM transitions for several values of $q$, and find the agreement with the hypothesis from the duality theory[3]. 1) Y. Ozeki and N. Ito, submitted to J. Phys. A\\ 2) A. B. Harris, J. Phys. C7 (1974) 1671\\ 3) K. Takeda, T. Sasamoto and H. Nishimori, J. Phys. A38 (2005) 3751.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Ozeki, Y.}, biburl = {https://www.bibsonomy.org/bibtex/2d1c109222bc05f6e8f11ea2a328003c7/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {e44951fecd71883adf78b854fe851daa}, intrahash = {d1c109222bc05f6e8f11ea2a328003c7}, keywords = {disordered fixed gauge glass ising j method model nonequilibrium point random relaxation statphys23 systems topic-9}, month = {9-13 July}, timestamp = {2007-06-20T10:16:24.000+0200}, title = {Nonequilibrium Relaxation Studies for Universality Classes and Random Fixed Point in Some Disordered Systems}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=592}, year = 2007 }