Exactly solvable spin ladder model with degenerate ferromagnetic and singlet states

We study the spin ladder model with interactions between spins on neighbori ng rungs. The model Hamiltonian with the exact singlet ground state degener ated with ferromagnetic state is obtained. The singlet ground state wave fu nction has a special recurrent form and depends on two parameters. Spin cor relations in the singlet ground state show double-spiral structure with per iod of spirals equals to the system size. For special values of parameters they have exponential decay. The spectrum of the model is gapless and there are asymptotically degenerated excited states for special values of parame ters in the thermodynamic limit.