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We introduce a model with conserved dynamics, where nearest neighbor pairs ofspins $\uparrow \downarrow (\downarrow \uparrow)$ can exchange to assume theconfiguration $\downarrow \uparrow (\uparrow \downarrow)$, with rate $\beta(\alpha)$, through energy decreasing moves only. We report exact solution forthe case when one of the rates, $\alpha$ or $\beta$, is zero. Theirreversibility of such dynamics results in strong dependence on the initialconditions. Domain wall arguments suggest that for more general models withsteady states the dynamical critical exponent for the anisotropic spin exchangeis different from the isotropic value.Comment: 16 pages, plain TeX fil

EXACT SOLUTION OF AN IRREVERSIBLE ONE-DIMENSIONAL MODEL WITH FULLY BIASED SPIN EXCHANGES