Direct Dynamical Evidence for the Spin Glass Lower Critical Dimension 2 < dl < 3

A dynamical method is introduced to study the effect of dimensionality on phase transitions. Direct experimental measurements for the lower critical dimension for spin glasses is provided as an example. The method makes use of the spin glass correlation length xi(t,T). Once nucleated, it can become comparable to sample dimensions in convenient time and temperature ranges. Thin films of amorphous Ge: Mn alloys were prepared with thickness L approximate to 15.5 nm. Conventional behavior is observed as long as xi(t,T) < L. At the measurement time t(co), when xi(t(co),T) approximate to L, the time dependence is observed to cross over to exponential. These results are interpreted using spin glass dynamics, and are consistent with a lower critical dimension for spin glasses, d(l), between 2 < d(l) < 3.