Domain Wall Renormalization Group Analysis of 2-dimensional Ising Model

Abstract

Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the 2-dimensional square lattice. For the lowest order approximation with two domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four domain wall states.

12 pages, 30 figures

References in corpus (3)

• Tensor renormalization group approach to 2D classical lattice models
• Tensor-entanglement renormalization group approach to 2D quantum systems
• High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

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