%0 Book Section %1 statphys23_0962 %A Vasin, M.G. %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 dynamical dynamics glass hypothesis scaling statphys23 topic-9 transition ultrametricity %T Description of Glass Transition in Terms of Critical Dynamics %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=962 %X In this work the attempt to describe the glass transition as a specific sort of phase transition in a disordered system using the critical dynamics method is undertaken. In order to do it, two main problems are solved: The order parameter, which allows us to use the scaling hypothesis to describe this transition, is defined; the method of description of the critical dynamics subject to dynamical ultrametricity 1 is suggested. In order to solve the first problem, liquid is represented as a complicated system of disclinations according to defect description of liquids and glasses 2, 3. The expressions for the linear disclination field of an arbitrary form and energy of inter-disclination interaction are derived in the framework of the gauge theory of defects. The formulated model represents the system of the randomly situated directors with dipole--dipole-like interaction. Just as in a nematic, in this system an ordering of directors occurs at freezing. However, as a result of their random situation a single direction for all topological moments of the system does not exist. But again it leads to the appearance of the topologically stable line defects (disclinations), corresponding to larger scales, already in the system of these directors. On every step of the freezing the successive correlation of the directors group occurs, which leads to the appearance of topological moments with a bigger scale. This hierarchy of the topological moments (vortices) determines scaling properties of the system. The glass transition is described in terms of critical dynamics taking into account the hierarchy of the intermodal relaxation times (dynamical ultrametricity) 5. The suggested model allows us to explain the slow dynamics in supercooled liquids close to the liquid-glass transition point. The Vogel-Fulcher-Tammann law for the system relaxation time is derived in terms of this approach. It is shown that the system satisfies the fluctuating-dissipative theorem in case of the absence of the intermodal relaxation time hierarchy. The choice of the topological moment as the order parameter is important in principle. On the one hand, it allows us to describe various physical systems within one model, while on the other hand, keeping the physical meaning of the scaling invariance principle. The obtained results indicate that the combination of approaches suggested above allows us to apply the scaling hypothesis and methods of critical dynamics to the description of glass transitions of the wide group of glass-forming systems: Super-cooled liquids, spin glasses, vortex glasses, and so on. This work was supported by the RFBR grants No. 07-02-00110-a and 07-02-96045-r-ural-a. 1) E. Bertin, and J.-P. Bouchaud, J. Phys.A: Math. Gen. Vol.35, 3039-3051 (2002);\\ 2) N. Rivier, D.M. Duffy, Numerical methods in the study of critical phenomena, Springer-Verlag, Berlin, Heidelberg, New York, 1981, pp. 132-142.\\ 3) D.R. Nelson, Phys.Rev.Lett., Vol.50, 982 (1983).\\ 4) M.G. Vasin, V.I. Lady'anov, J.Phys.:Condens.Matter., Vol.17 S1287-S1292 (2005).\\ 5) M.G. Vasin, Phys.Rev.B Vol.74, p.214116 (2006).

@incollection{statphys23_0962, abstract = {In this work the attempt to describe the glass transition as a specific sort of phase transition in a disordered system using the critical dynamics method is undertaken. In order to do it, two main problems are solved: The order parameter, which allows us to use the scaling hypothesis to describe this transition, is defined; the method of description of the critical dynamics subject to dynamical ultrametricity [1] is suggested. In order to solve the first problem, liquid is represented as a complicated system of disclinations according to defect description of liquids and glasses [2, 3]. The expressions for the linear disclination field of an arbitrary form and energy of inter-disclination interaction are derived in the framework of the gauge theory of defects. The formulated model represents the system of the randomly situated directors with dipole--dipole-like interaction. Just as in a nematic, in this system an ordering of directors occurs at freezing. However, as a result of their random situation a single direction for all topological moments of the system does not exist. But again it leads to the appearance of the topologically stable line defects (disclinations), corresponding to larger scales, already in the system of these directors. On every step of the freezing the successive correlation of the directors group occurs, which leads to the appearance of topological moments with a bigger scale. This hierarchy of the topological moments (vortices) determines scaling properties of the system. The glass transition is described in terms of critical dynamics taking into account the hierarchy of the intermodal relaxation times (dynamical ultrametricity) [5]. The suggested model allows us to explain the slow dynamics in supercooled liquids close to the liquid-glass transition point. The Vogel-Fulcher-Tammann law for the system relaxation time is derived in terms of this approach. It is shown that the system satisfies the fluctuating-dissipative theorem in case of the absence of the intermodal relaxation time hierarchy. The choice of the topological moment as the order parameter is important in principle. On the one hand, it allows us to describe various physical systems within one model, while on the other hand, keeping the physical meaning of the scaling invariance principle. The obtained results indicate that the combination of approaches suggested above allows us to apply the scaling hypothesis and methods of critical dynamics to the description of glass transitions of the wide group of glass-forming systems: Super-cooled liquids, spin glasses, vortex glasses, and so on. This work was supported by the RFBR grants No. 07-02-00110-a and 07-02-96045-r-ural-a. 1) E. Bertin, and J.-P. Bouchaud, J. Phys.A: Math. Gen. Vol.35, 3039-3051 (2002);\\ 2) N. Rivier, D.M. Duffy, Numerical methods in the study of critical phenomena, Springer-Verlag, Berlin, Heidelberg, New York, 1981, pp. 132-142.\\ 3) D.R. Nelson, Phys.Rev.Lett., Vol.50, 982 (1983).\\ 4) M.G. Vasin, V.I. Lady'anov, J.Phys.:Condens.Matter., Vol.17 S1287-S1292 (2005).\\ 5) M.G. Vasin, Phys.Rev.B Vol.74, p.214116 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Vasin, M.G.}, biburl = {https://www.bibsonomy.org/bibtex/260acd66c0c7cb36272b5837de10dbeb1/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {273c1660aa51d6c98a4db06c755a439c}, intrahash = {60acd66c0c7cb36272b5837de10dbeb1}, keywords = {critical dynamical dynamics glass hypothesis scaling statphys23 topic-9 transition ultrametricity}, month = {9-13 July}, timestamp = {2007-06-20T10:16:35.000+0200}, title = {Description of Glass Transition in Terms of Critical Dynamics}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=962}, year = 2007 }