Nonlinear σ model at θ=π: Euclidean lattice formulation and solid-on-solid models

We study the strong-coupling expansion of a Euclidean lattice formulation of the two-dimensional O(3) {σ}-model at nonzero topological angle {θ}, mapping it onto a solid-on-solid model with well-known critical behavior. The results are consistent with those predicted by the mapping of the Hamiltonian formulation of the {σ} model onto quantum spin chains. The model has a gapless phase at {θ}={π} and weak coupling in which a condensate of Coleman's ``half-asymptotic'' particles exists.