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Abstract: We have studied the ground state and thermodynamic properties of the anisotropic 3-state Potts model on square lattice by means of the tensor network-based numerical method. The phase diagrams of this model in the ground state and at finite temperature are identified. The singular behavior at the critical endpoint along the phase boundary is carefully investigated. It is discovered that the sharp peaks appear in the second-order derivative of the field as well as the first-order derivative of the magnetization with respect to temperature on the phase boundary. Our numerical results confirm the prediction of Fisher et al. about the critical endpoint. [Copyright &y& Elsevier]

Abstract: By the infinite time-evolving block decimation (iTEBD) technique, the magnetization process in spin-1 Ising model with single-ion anisotropy under external field is investigated in the thermodynamic limit. An updated phase diagram is proposed, and the detailed magnetic structures of the phase diagram are uncovered. It must be noted that two interesting phases with same magnetization plateau (M z =0) but different magnetic structures are distinguished. Furthermore, they are verified to be an ideal Néel phase and an ideal large-D phase respectively. In addition, a first-order quantum phase transition line between them is determined to be at D=1. [Copyright &y& Elsevier]