Se p 19 99 Phase diagram of the 1 2 - 1 2 - 1 - 1 spin chain by the nonlinear σ model

We examine a periodic mixed spin chain with spin magnitudes 1 2 and 1 which are arrayed as 1 2 1 2 -1-1. The three independent parameters are ratios of the four exchange couplings. We determine phase boundaries in the parameter space by using the gapless condition which was previously derived by mapping a general inhomogeneous spin chain to the nonlinear σ model. We find two gapless boundaries separating three disordered phases. The features of the phases are explained in terms of singlet clusters.