Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains

We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains with an antiferromagnetic coupling along the chains. It is shown that the system always has a spectral gap. For the case of identical chains the model in the continuous limit is equivalent to 4 decoupled noncritical Ising models. For this case we obtain the exact expressions for the asymptotics of spin-spin correlation functions. When the chains have different exchange integrals the spectrum at low energies is well described by the O(3) nonlinear sigma model. We discuss the topological order parameter related to the gap formation and give a detailed description of the dynamical magnetic susceptibility.