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

We apply the higher-order tensor renormalization group to the four-dimensional ferromagnetic Ising model, which has been attracting interest in the context of the triviality of the scalar ϕd=44 theory. We investigate the phase transition of this model with the higher-order tensor renormalization group enlarging the lattice size up to 10244 with parallel computation. The results for the internal energy and the magnetization are consistent with the weak first-order phase transition.