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Register a new userTensor network analysis of critical coupling in two dimensional $phi^{4}$ theory
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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 observables without statistical uncertainties. We determine the critical coupling in the continuum limit employing the tensor network formulation for scalar field theories proposed in our previous paper. We obtain $left[ lambda / mu_{mathrm{c}}^{2} right]_{mathrm{cont.}} = 10.913(56)$ with the quartic coupling $lambda$ and the renormalized critical mass $mu_{mathrm{c}}$. The result is compared with previous results obtained by different approaches.
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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 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 critical point. Since it is expected to be a direct outcome of an imaginary part of the action, an approach free from the sign problem is needed. We study this model systematically changing the chemical potential in order to check the applicability of the tensor renormalization group to the model in which scalar fields are discretized by the Gaussian quadrature. The Silver Blaze phenomenon is successfully confirmed on the extremely large volume $V=1024^2$ and the results are also ensured by another tensor network representation with a character expansion.
We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition to be 0.89290(5) which is an improvement compared to earlier studies using tensor network methods.
We show that the exact beta-function beta(g) in the continuous 2D gPhi^{4} model possesses the Kramers-Wannier duality symmetry. The duality symmetry transformation tilde{g}=d(g) such that beta(d(g))=d(g)beta(g) is constructed and the approximate values of g^{*} computed from the duality equation d(g^{*})=g^{*} are shown to agree with the available numerical results. The calculation of the beta-function beta(g) for the 2D scalar gPhi^{4} field theory based on the strong coupling expansion is developed and the expansion of beta(g) in powers of g^{-1} is obtained up to order g^{-8}. The numerical values calculated for the renormalized coupling constant g_{+}^{*} are in reasonable good agreement with the best modern estimates recently obtained from the high-temperature series expansion and with those known from the perturbative four-loop renormalization-group calculations. The application of Cardys theorem for calculating the renormalized isothermal coupling constant g_{c} of the 2D Ising model and the related universal critical amplitudes is also discussed.
In this contribution we present an exploratory study of several novel methods for numerical stochastic perturbation theory. For the investigation we consider observables defined through the gradient flow in the simple {phi}^4 theory.
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