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 (spin ladder). It is shown that the system always has a spectral gap and the lower lying excitations are triplets, For the case of identical chains the model in the continuous limit is shown to be equivalent to four decoupled noncritical Ising models with the Z(2)xSU(2) symmetry. For this case we obtain the exact expressions for asymptotics of spin-spin correlation functions. It is shown that when the chains have different exchange integrals J(1) much greater than J(2) the spectrum at low energies is 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.