The low-temperature properties of the spin $S=1/2$ ladder with anisotropic ferromagnetic legs are studied using the continuum limit Bosonization approach. The weak-coupling ground-state phase diagram of the model is obtained for a wide range of coupling constants and several unconventional gapless ``spin liquid'' phases are shown to exist for ferromagnetic coupling. The behavior of the ladder system in the vicinity of the ferromagnetic instability point is discussed in detail.
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Vekua et al. (2003) studied this question.
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