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September 23, 2019Open Access

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

Key Points

This research aims to explore the phase transition of the four-dimensional ferromagnetic Ising model using the higher-order tensor renormalization group.
Applied higher-order tensor renormalization group to the four-dimensional Ising model
Increased lattice size to 1024^4 using parallel computation
Focused on analyzing internal energy and magnetization
Findings indicate a weak first-order phase transition
Internal energy and magnetization results are consistent with theoretical expectations
Results stem from extensive lattice configurations and computations

Abstract

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 ₃=₄^4 theory. We investigate the phase transition of this model with the higher-order tensor renormalization group 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.

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