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

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.

arXiv comment7 pages, 10 figures, Proceedings of the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China

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Cited by in corpus (6)

• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Tensor renormalization group approach to four-dimensional complex ${\varphi }^4$ theory at finite density
• Tensor renormalization group study of (3+1)-dimensional $Z_2$ gauge-Higgs model at finite density
• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• Matrix product decomposition for two- and three-flavor Wilson fermions: Benchmark results in the lattice Gross-Neveu model at finite density
• Triad representation for the anisotropic tensor renormalization group in four dimensions