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We study the three-dimensional $SU(2)$ principal chiral model (PCM) usingdifferent tensor renormalization group methods based on the triad andanisotropic decomposition of the tensor. The tensor network representation isformulated based on the character expansion of the Boltzmann weight. We comparethe average action obtained using these two tensor network algorithms andconfirm that the resulting critical coupling and exponent are comparable withthe recent estimations from the Monte Carlo methods.

Tensor renormalization group study of 3D principal chiral model