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arXiv:2101.06953 · Physical review. D/Physical review. D.

Phase transition of four-dimensional lattice ϕ4 theory with tensor renormalization group

Shinichiro Akiyama, Y. Kuramashi, Yusuke Yoshimura

Published Aug 30, 2021• 20 citations
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Abstract

We investigate the phase transition of the four-dimensional single-component ${\ensuremath{\phi}}^{4}$ 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 $⟨\ensuremath{\phi}⟩$ at a finite quartic coupling $\ensuremath{\lambda}$ on large volumes up to $V=102{4}^{4}$ 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 ${\ensuremath{\phi}}^{4}$ theory and find that the properties of the phase transition are consistent with the universality class of the three-dimensional Ising model.

DOI
10.1103/physrevd.104.034507

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The behavior of dimensionless quantities defined as ratios of partition functions is analyzed to investigate phase transitions and critical phenomena. At criticality, the universal values of these ratios can be predicted from conformal field theory (CFT) through the modular-invariant partition functions on a torus. We perform numerical calculations using the bond-weighted tensor renormalization group for three two-dimensional models belonging to different universality classes: the Ising model, the three-state Potts model, and the four-state Potts model. The partition-function ratios obey the same finite-size scaling form as the Binder parameter, and their critical values agree well with the universal values predicted by CFT. In the four-state Potts model, we observe logarithmic corrections in the system-size dependence of these ratios.
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