Analyticity properties of the weakly coupled double-well model

In this note we study lattice Φ⁴-models with Hamiltonian $$H = tfrac{1}{2}(varphi , - Delta varphi ) + lambda Sigma left( {varphi _i^2 - frac{{m^2 }}{{8lambda }}} right)^2$$ and Gaussian boundary conditions. Using the polymer expansion we obtain analyticity of the pressure and the correlation functions in the infinite volume limit in a region $$left{ {left. lambda right| left| lambda right|< varepsilon ,left| {arg } right.left. lambda right|< frac{pi }{2} - delta } right}$$ for every δ>0.