Spin dynamics and glassy relaxation on fractals and percolation structures

Single-spin-flip dynamics of discrete spin models on fractals and percolation structures is studied within the framework of a low temperature approach. Using a scaling theory we show that, in general, the energy barrier for overturning a finite cluster of s spins scales as In s. The probability distribution of the energy barriers for percolation clusters is argued to be given by the extreme-value distribution. The resulting long time relaxational dynamics so obtained is a stretched exponential with a temperature dependent exponent. Our results lead to a natural formulation of a new dynamic scaling hypothesis and are discussed in relation with the so-called glassy dynamics.