Investigation of frustrated and dimerized classical Heisenberg chains

We have considered the 1D dimerized frustrated antiferromagnetic (ferromagnetic) Heisenberg model with arbitrary spin S$S$. 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${\alpha }_c=\pm 0.25$, a well-known result. In the vicinity of the critical points _αc${\alpha }_c$, the exact classical critical exponent of the spiral order parameter is found to be 1/2$1/2$. In the case of a dimerized chain (δ≠0$\delta \ne 0$), 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.