  The aim of the present article is to explicitly compute parameters for which
the Bramson-Kalikow model exhibits phase-transition. The main ingredient of the
proof is a simple new criterion for non-uniqueness of $g$-measures. We show
that the existence of multiple $g$-measures compatible with a function $g$ can
be proved by estimating the $\bar{d}$-distances between some suitably chosen
Markov chains. The method is optimal for the important class of binary regular
attractive functions, which includes the Bramson-Kalikow model.
