Exact Solution of an Irreversible One-Dimensional Model with Fully Biased Spin Exchanges

We introduce a model with conserved dynamics, where nearest neighbor pairs of spins $\uparrow \downarrow (\downarrow \uparrow)$ can exchange to assume the configuration $\downarrow \uparrow (\uparrow \downarrow)$, with rate $\beta (\alpha)$, through energy decreasing moves only. We report exact solution for the case when one of the rates, $\alpha$ or $\beta$, is zero. The irreversibility of such dynamics results in strong dependence on the initial conditions. Domain wall arguments suggest that for more general models with steady states the dynamical critical exponent for the anisotropic spin exchange is different from the isotropic value.