Counting independent sets on bipartite graphs (#BIS) is considered a
canonical counting problem of intermediate approximation complexity. It is
conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to
approximate. We study #BIS in the general framework of two-state spin systems
on bipartite graphs. We define two notions, nearly-independent phase-correlated
spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate
the partition function of any 2-spin system on bipartite graphs supporting
these two notions. As a consequence, we classify the complexity of
approximating the partition function of antiferromagnetic 2-spin systems on
bounded-degree bipartite graphs