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

## TL;DR

This paper uses the higher-order tensor renormalization group to study the four-dimensional Ising model, revealing a weak first-order phase transition through large-scale simulations.

## Contribution

It applies HOTRG to a 4D Ising model at unprecedented lattice sizes, providing new insights into its phase transition nature.

## Key findings

- Results indicate a weak first-order phase transition.
- Simulations performed on lattices up to 1024^4.
- Internal energy and magnetization data support the transition type.

## 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 $\phi^4_{d=4}$ 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.