  Statistical behavior of a classical $\phi ^{4}$ Hamiltonian lattice is
investigated from microscopic dynamics. The largest Lyapunov exponent and
entropies are considered for manifesting chaos and equipartition behaviors of
the system. It is found, for the first time, that for any large while finite
system size there exist two critical couplings for the transitions to
equipartitions, and the scaling behaviors of these lower and upper critical
couplings vs the system size is numerically obtained.
