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The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the computational cost scales logarithmically with the space-time volume. This fact allows us to aggressively approach the thermodynamic limit. While taking this advantage, we study the critical coupling of the two dimensional $phi^{4}$ theory on large and fine lattices. We present the numerical results along with the extrapolation procedure to the continuum limit and compare them with the previous ones by Monte Carlo simulations.
We make a detailed analysis of the spontaneous $Z_{2}$-symmetry breaking in the two dimensional real $phi^{4}$ theory with the tensor renormalization group approach, which allows us to take the thermodynamic limit easily and determine the physical ob
The quantum extension of classical finite elements, referred to as quantum finite elements ({bf QFE})~cite{Brower:2018szu,Brower:2016vsl}, is applied to the radial quantization of 3d $phi^4$ theory on a simplicial lattice for the $mathbb R times math
Supersymmetric models with spontaneous supersymmetry breaking suffer from the notorious sign problem in stochastic approaches. By contrast, the tensor network approaches do not have such a problem since they are based on deterministic procedures. In
We compute numerically the effective potential for the $(lambda Phi^4)_4$ theory on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. Two different methods for obtaining the effecti
We study the two-dimensional complex $phi^{4}$ theory at finite chemical potential using the tensor renormalization group. This model exhibits the Silver Blaze phenomenon in which bulk observables are independent of the chemical potential below the c