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arXiv:hep-th/9507159 · Physical Review Letters

Critical Equation of State from the Average Action

Jürgen Berges, N. Tetradis, CHRISTOF WETTERICH

Published Jul 29, 1996• 78 citations
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Abstract

The scaling form of the critical equation of state is computed for $O(N)$-symmetric models. We employ a method based on an exact flow equation for a coarse-grained free energy. A suitable truncation is solved numerically.

DOI
10.1103/physrevlett.77.873

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arXiv:2305.09899•May 17, 2023•4 citations
The scaling form of the critical equation of state is computed for O(N)O(N)O(N)-symmetric models. We employ a method based on an exact flow equation for a coarse-grained free energy. A suitable truncation is solved numerically.
We present a comprehensive study on the extraction of CFT data using tensor network methods, specially, from the fixed-point tensor of the linearized tensor renormalization group (lTRG) for the 2D classical Ising model near the critical temperature. Utilizing two different methods, we extract operator scaling dimensions and operator-product-expansion (OPE) coefficients by introducing defects on the lattice and by employing the fixed-point tensor. We also explore the effects of point-like defects in the lattice on the coarse-graining process. We find that there is a correspondence between coarse-grained defect tensors and conformal states obtained from lTRG fixed-point equation. We also analyze the capabilities and limitations of our proposed coarse-graining scheme for tensor networks with point-like defects, which includes graph independent local truncation (GILT) and higher-order tensor renormalization group (HOTRG). Our results provide a better understanding of the capacity and limitations of the tenor renormalization group scheme in coarse-graining defect tensors, and we show that GILT+HOTRG can be used to give accurate two- and four-point functions under specific conditions. We also find that employing the minimal canonical form further improves the stability of the RG flow.