Zigzag spin chains with antiferromagnetic-ferromagnetic interactions:   Transfer-matrix renormalization group study
  Properties of the zigzag spin chains with various nearest-neighbor and next-nearest-neighbor interactions are studied by making use of the transfer-matrix renormalization group method. Thermodynamic quantities of the systems (temperature dependence of the susceptibility and the specific heat), as well as the field dependence of the magnetization are analyzed numerically with a high accuracy in the thermodynamic limit. The results have been compared with the recent experimental data on Rb$_2$Cu$_{2}$Mo$_{3}$O$_{12}$. 
H. T. Lu, Y. J. Wang, Shaojin Qin, T. Xiang