Phase transition of four-dimensional Ising model with higher-order tensor renormalization group

Abstract

We apply the higher-order tensor renormalization group (HOTRG) to the four-dimensional ferromagnetic Ising model, which has been attracting interests in the context of the triviality of the scalar ${\varphi }_{d=4}^4$ theory. We investigate the phase transition of this model with HOTRG enlarging the lattice size up to $1024^4$ with parallel computation. The results for the internal energy and the magnetization are consistent with the weak first-order phase transition.

Comments: 14 pages, 7 figures