Ring exchange in low-dimensional spin systems

Abstract The isotropic S= 1 2 antiferromagnetic spin ladder with additional four-spin ring exchange is studied perturbatively in the strong coupling regime with the cluster expansion technique, and by bosonization in the weak coupling limit. It is found that a sufficiently large amount of ring exchange leads to a second-order phase transition into a spontaneously dimerized phase. The shape of the phase boundary in the vicinity of the exactly known transition point is obtained. The relevance of ring exchange for materials with 2D CuO 2 planes is discussed.