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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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Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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. Cost Reduction of Swapping Bonds Part in Anisotropic Tensor Renormalization Group

    cond-mat.stat-mech 2019-08 conditional novelty 6.0 of 10

    An alternative swapping-bonds step lowers the bottleneck cost of ATRG from O(chi^(2d+1)) to O(chi^max(d+3,7)) and the memory from O(chi^(2d)) to O(chi^max(d+1,6)), with matching 4D Ising results.

  3. 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) ...

  4. Applying the Triad network representation to four-dimensional ATRG method

    hep-lat 2024-12 conditional novelty 5.0 of 10

    Triad-ATRG applies the triad and MDTRG decomposition to four-dimensional ATRG, reducing the contraction cost to O(r^2 χ^7) while reproducing ATRG free energies and transition temperatures.

  5. Ward-constrained melonic renormalization group flow for the rank-four $\phi^6$ tensorial group field theory

    hep-th 2019-08 reject novelty 4.0 of 10

    For the rank-4 φ6 tensorial group field theory, the authors derive a Ward-constrained renormalization group flow and report a nontrivial fixed point, but the fixed point's reported values violate their own consistency...

  6. Tensor renormalization group study of (1+1)-dimensional O(3) nonlinear sigma model with and without finite chemical potential

    hep-lat 2024-12 conditional novelty 2.0 of 10

    Tensor renormalization group yields central charge c = 1.97(9) and critical exponents nu = 0.512(15), z = 1.96(6) for the (1+1)d O(3) sigma model, matching theory.

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