In spin glasses, the interplay of disorder and frustrated exchange interactions between spins leads to exceptionally slow spin relaxation and intrinsically non-equilibrium (aging) dynamics. We have introduced a new approach to understanding the aging dynamics of short-range spin glass models. This is based on our observation that the aging dynamics of such models have a symmetry under time reparametrizations, and has led us to identify the soft modes in the system as spatially varying time reparametrizations. This can be understood more simply in an analogy with rotation invariance in a ferromagnet. Starting from this invariance leads to a number of predictions that are in good agreement with numerical simulations. These results for spin glasses may prove useful in understanding dynamic heterogeneities in other glassy systems.

"Heterogeneous slow dynamics in a two dimensional doped classical antiferromagnet",
M. P. Kennett, C. Chamon, and L. F. Cugliandolo, Phys. Rev. B 72 024417 (2005). cond-mat/0410734.  

"Spatially heterogeneous ages in glassy dynamics",
H. E. Castillo, C. Chamon, L. F. Cugliandolo, J. L. Iguain and M. P. Kennett, Phys. Rev. B 68, 134442 (2003). cond-mat/0211558.  

"Separation of time scales and reparametrization invariance for aging systems",
C. Chamon, M. P. Kennett, H. E. Castillo, and L. F. Cugliandolo, Phys. Rev. Lett. 89, 217201 (2002). cond-mat/0109150

"Heterogeneous Aging in Spin Glasses",
H. E. Castillo, C. Chamon, L. F. Cugliandolo and M. P. Kennett, Phys. Rev. Lett. 88 , 237201 (2002).   cond-mat/0112272  

"Aging of spin glasses of quantum rotors",
M. P. Kennett, C. Chamon and J. Ye, Phys. Rev. B 64, 224408 (2001).   cond-mat/0103428

"Time reparametrization group and the long time behaviour in quantum glassy systems",
M. P. Kennett and C. Chamon, Phys. Rev. Lett. 86, 1622 (2001).    cond-mat/0009099 .

Kinetically constrained spin models are known to exhibit dynamical behavior mimicking that of glass forming systems. They are often understood as coarse-grained models of glass formers, in terms of some "mobility" field. The identity of this "mobility" field has remained elusive due to the lack of coarse-graining procedures to obtain these models from a more microscopic point of view. We exhibit a scheme to map the dynamics of a two-dimensional soft disc glass former onto a kinetically constrained spin model, providing an attempt at bridging these two approaches.