On kinetic Ising models in one dimension

It is shown that Glauber dynamics in 1D Ising spin systems is not universal. This is illustrated on a periodic model with a basic unit cell (J 1 ,. . ., J n ) containing an arbitrary set of n ferromagnetic coupling constants. The dynamic critical exponent z is calculated exactly as z=1+max(J i )/min(J i ), the known value z=2 is recovered only for n=1. The extension of this result to other types of dynamics is briefly discussed.