Investigation of the Potts Model on Triangular Lattices by the Second Renormalization of Tensor Network States

We employ the second renormalization group method of tensor-network states to investigate thermodynamic properties of the ferromagnetic and antiferromagnetic Potts model on triangular lattices. From the temperature dependence of the internal energy and the specific heat, both the critical temperatures and critical exponents are evaluated. For the q=3 antiferromagnetic Potts model, the critical temperature is found to be T_c = 0.627163 ±0.000003, which is at least one order of magnitude more accurate than that obtained by other methods.