Phase transition of four-dimensional Ising model with tensor network scheme

Shinichiro Akiyama; Takumi Yamashita; Yoshinobu Kuramashi; Yusuke Yoshimura

Phase transition of four-dimensional Ising model with tensor network scheme

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arxiv 1911.12954 v1 pith:UO4YTTPC submitted 2019-11-29 hep-lat

Shinichiro Akiyama , Yoshinobu Kuramashi , Takumi Yamashita , Yusuke Yoshimura This is my paper · ORCID

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keywords tensorphasetransitionalgorithmfour-dimensionalgroupisingmodel

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abstract

We investigate the phase transition of the four-dimensional Ising model with two types of tensor network scheme, one is the higher-order tensor renormalization group and the other is the anisotropic tensor renormalization group. The results for the internal energy and magnetization obtained by the former algorithm with the impure tensor method, enlarging the lattice volume up to $1024^4$, are consistent with the weak first-order phase transition. For the later algorithm, our implementation successfully reduces the execution time thanks to the parallel computation and the results provided by ATRG seems comparable to those with HOTRG.

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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.

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