Phase transition of four-dimensional Ising model with tensor network scheme

TL;DR

This paper explores phase transitions in the four-dimensional Ising model using advanced tensor network schemes, demonstrating consistency with weak first-order transitions and improving computational efficiency.

Contribution

It introduces and compares two tensor network algorithms for analyzing the 4D Ising model, highlighting their effectiveness and computational advantages.

Findings

Results align with weak first-order phase transition

Enlarged lattice volume up to 1024^4

Reduced execution time through parallel computation

Abstract

We investigate the phase transition of the four-dimensional Ising model with two types of tensor network scheme, one is the higher-order tensor renormalization group and the other is the anisotropic tensor renormalization group. The results for the internal energy and magnetization obtained by the former algorithm with the impure tensor method, enlarging the lattice volume up to $1024^4$, are consistent with the weak first-order phase transition. For the later algorithm, our implementation successfully reduces the execution time thanks to the parallel computation and the results provided by ATRG seems comparable to those with HOTRG.