Abstract
The dynamic critical behaviour of spin systems with quenched impurities, and of amorphous spin systems as characterized by the additional presence of random anisotropy directions, is studied by renormalization group methods to second order inε=4−d. For the Halperin-Hohenberg-Ma model with purely relaxational dynamics it is concluded that in three dimensions (d=3) the critical slowing down should be enhanced by impurities for systems with Ising type statics, whereas there is no change forXY- and Heisenberg systems. For amorphous systems, however, the critical dynamics should change also in theXY- and Heisenberg cases. Furthermore, it is concluded that additional conserved, but noncritical modes become always statically decoupled from the order parameter for systems with impurities, but not for amorphous systems. Thus, for the impure system, the energy density mode and the asymmetric models of Halperin, Hohenberg and Siggia are ruled out. But the effects of dynamic coupling remain: Especially, the relationz=d/2 for the dynamic exponent of planar and isotropic antiferromagnets is modified for impure or amorphous systems.
Similar content being viewed by others
References
Harris, A.B., Lubensky, T.C., Chen, J.H.: Phys. Rev. Lett.36, 415 (1976)
Aharony, A.: Phys. Rev. B12, 1038 (1975)
Aharony, A.: Phys. Rev. B12, 1049 (1975)
Lubensky, T.C.: Phys. Rev. B11, 3573 (1975)
Grinstein, G., Luther, A.: Phys. Rev. B13, 1329 (1976)
Krey, U.: Physica80B, 231 (1975)
Krey, U.: Phys. Lett.51 A, 189 (1975)
Krey, U.: Physica83B, 349 (1976)
Stephen, M.J.: Phys. Lett.55 A, 273 (1975)
McCoy, B., in: Phase Transitions and Critical Phenomena, Vol. 2, (C. Domb and M.S. Green, eds.) London-New York: Academic Press 1972
Rauh, A.: Phys. Rev. B13, 2089 (1976)
Griffiths, R.B.: Phys. Rev. Lett.23, 17 (1969)
Harris, A.B.: Phys. Rev. B12, 203 (1975)
Wortis, M.: Phys. Rev. B11, 4665 (1974)
Halperin, B.I., Hohenberg, P.C., Ma, S.K.: Phys. Rev. B10, 139 (1974)
Halperin, B.I., Hohenberg, P.C., Siggia, D.E.: Phys. Rev. B13, 1299 (1976)
Sasvári, L., Szépfalusy, P.: preprint
Freedman, R., Mazenko, G.F.: Phys. Rev. B13, 4967 (1976)
Janssen, K.H., preprint
Harris, R., Plischke, M., Zuckermann, M.J.: Phys. Rev. Lett.31, 160 (1973)
Ma, S.K., Mazenko, G.F.: Phys. Rev. B11, 4077 (1975)
Bausch, R., Janssen, H.K., Wagner, H.: Z. Physik B24, 113 (1976)
Martin, P.C., Siggia, E.D., Rose, H.A.: Phys. Rev. A8, 423 (1973)
De Dominicis, C.: Lett. Nuovo Cim.12, 567 (1975)
Wilson, K.G., Kogut, J.: Phys. Report12c, 77 (1974)
Callan, C.G., Jr.: Phys. Rev. D2, 1541 (1970); Symanzik, K.: Comm. Math. Phys.18, 227 (1970);23, 49 (1971)
Brézin, E., Le Guillou, J.C., Zinn-Justin, J.: In: Phase Transitions and Critical Phenomena, Vol. 6, (C. Domb and M.S. Green, eds.) London-New York: Academic Press (to be published)
Bruce, A., Droz, M., Aharony, A.: J. Phys. C7, 3673 (1974)
Chen, J., Lubensky, T.C.: preprint
Krey, U.: Phys. Lett.57 A, 215 (1976)
Krey, U.: Proceedings of the ICM 76, to be published in Physica B
Krey, U.: unpublished
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Krey, U. On the critical dynamics of disordered spin systems. Z Physik B 26, 355–366 (1977). https://doi.org/10.1007/BF01570746
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01570746