  The results of extensive histogram cluster heat-bath Monte Carlo simulations
on the critical behavior of the quasi-one dimensional Ising antiferromagnet on
a stacked triangular lattice are presented. A small applied field is shown to
induce a crossover from XY universality to mean-field tricritical behavior.
Experimental estimates of critical exponents suggest that these two types of
phase transitions are observed in S=1 CsNiCl$_3$ and $S=1/2$ CsCoBr$_3$,
respectively. The present results demonstrate that this difference can be
explained by an unusual staggered magnetic field arising from quantum exchange
mixing previously proposed to account for spin excitations in $S=1/2$
quasi-one-dimensional Ising antiferromagnets.
