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

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arxiv 1906.06060 v2 pith:HIHG32HB submitted 2019-06-14 hep-lat

Shinichiro Akiyama , Yoshinobu Kuramashi , Takumi Yamashita , Yusuke Yoshimura This is my paper · ORCID
classification hep-lat
keywords modelphasetransitionfour-dimensionalgrouphigher-orderhotrgising
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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.

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Cited by 2 Pith papers

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  1. Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method

    hep-lat 2026-02 conditional novelty 7.0 of 10

    Forward-mode AD for TRG is derived with (k+1)(k+2)/2 cost scaling, linked to impurity methods, and tested on the 2D/3D Ising model for energy, specific heat, and critical exponents.

  2. Twisted Partition Functions as Order Parameters

    hep-th 2025-05 conditional novelty 5.0 of 10

    Twisted partition functions work as an order parameter that separates broken-symmetry, symmetry-protected, and symmetry-enriched phases, reproduce the Wilson-'t Hooft classification in 4d gauge theories, and tie U(1) ...

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