Phase transitions in the Heisenberg spin ladder with ferromagnetic legs

Phase transitions in weakly anisotropic spin ladders with antiferromagnetically coupled ferromagnetic legs are studied in the framework of a nonlinear $\sigma$-model approach. It has been found that the system behaves like an integer-spin antiferromagnetic chain, and the phase transition into the antiferomagnetically ordered state is possible only above some critical anisotropy value, which depends exponentially on the strength of the ferromagnetic interaction in the legs. The theoretical predictions qualitatively agree with recent numerical results.