  We study the chromatic polynomials (= zero-temperature antiferromagnetic
Potts-model partition functions) P_G(q) for m \times n rectangular subsets of
the square lattice, with m \le 8 (free or periodic transverse boundary
conditions) and n arbitrary (free longitudinal boundary conditions), using a
transfer matrix in the Fortuin-Kasteleyn representation. In particular, we
extract the limiting curves of partition-function zeros when n \to\infty, which
arise from the crossing in modulus of dominant eigenvalues (Beraha-Kahane-Weiss
theorem). We also provide evidence that the Beraha numbers B_2,B_3,B_4,B_5 are
limiting points of partition-function zeros as n \to\infty whenever the strip
width m is \ge 7 (periodic transverse b.c.) or \ge 8 (free transverse b.c.).
Along the way, we prove that a noninteger Beraha number (except perhaps B_{10})
cannot be a chromatic root of any graph.
