Investigation of frustrated and dimerized classical Heisenberg chains

We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenberg model with arbitrary spin S. The exact classical magnetic phase diagram at zero temperature is determined using the LK cluster method. The cluster method results show that the classical ground-state phase diagram of the model is very rich, including first-order and second-order phase transitions. In the absence of dimerization, a second-order phase transition occurs between antiferromagnetic (ferromagnetic) and spiral phases at the critical frustration αc=±0.25, a well-known result. In the vicinity of the critical points αc, the exact classical critical exponent of the spiral order parameter is found to be 1/2. In the case of a dimerized chain (δ≠0), the spiral order shows stability and exists in some part of the ground-state phase diagram. We have found two first-order phase boundaries separating antiferromagnetic (uud and duu) phases from the spiral phase.