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arXiv · 2101.06953

Phase transition of four-dimensional lattice $\phi^4$ theory with tensor renormalization group

Shinichiro Akiyama·Yoshinobu Kuramashi·Yusuke Yoshimura
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Abstract

We investigate the phase transition of the four-dimensional single-component $\phi^4$ theory on the lattice using the tensor renormalization group method. We have examined the hopping parameter dependence of the bond energy and the vacuum condensation of the scalar field $\langle\phi\rangle$ at a finite quartic coupling $\lambda$ on large volumes up to $V=1024^4$ in order to detect the spontaneous breaking of the $\mathbb{Z}_2$ symmetry. Our results show that the system undergoes the weak first-order phase transition at a certain critical value of the hopping parameter. We also make a comparative study of the three-dimensional $\phi^4$ theory and find that the properties of the phase transition are consistent with the universality class of the three-dimensional Ising model.

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Shinichiro Akiyama, Yoshinobu Kuramashi, Yusuke Yoshimura. 2021-01-18. Phase transition of four-dimensional lattice $\phi^4$ theory with tensor renormalization group. https://doi.org/10.1103/physrevd.104.034507

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