  We investigate the topological charge in 1+1 dimensional $\phi^4$ theory on a
lattice with Anti Periodic Boundary Condition (APBC) in the spatial direction.
We propose a simple order parameter for the lattice theory with APBC and we
demonstrate its effectiveness. Our study suggests that kink condensation is a
possible mechanism for the order-disorder phase transition in the 1+1
dimensional $\phi^4$ theory. With renormalizations performed on the lattice
with Periodic Boundary Condition (PBC), the topological charge in the
renormalized theory is given as the ratio of the order parameters in the
lattices with APBC and PBC. We present a comparison of topological charges in
the bare and the renormalized theory and demonstrate invariance of the charge
of the renormalized theory in the broken symmetry phase.
