  We prove Gibbs distribution of two-state spin systems(also known as binary
Markov random fields) without hard constrains on a tree exhibits strong spatial
mixing(also known as strong correlation decay), under the assumption that, for
arbitrary `external field', the absolute value of `inverse temperature' is
small, or the `external field' is uniformly large or small. The first condition
on `inverse temperature' is tight if the distribution is restricted to
ferromagnetic or antiferromagnetic Ising models.
  Thanks to Weitz's self-avoiding tree, we extends the result for sparse on
average graphs, which generalizes part of the recent work of Mossel and
Sly\cite{MS08}, who proved the strong spatial mixing property for ferromagnetic
Ising model. Our proof yields a different approach, carefully exploiting the
monotonicity of local recursion. To our best knowledge, the second condition of
`external field' for strong spatial mixing in this paper is first considered
and stated in term of `maximum average degree' and `interaction energy'. As an
application, we present an FPTAS for partition functions of two-state spin
models without hard constrains under the above assumptions in a general family
of graphs including interesting bounded degree graphs.
