Improved phenomenological renormalization schemes

@article{Yurishchev2000ImprovedPR,
  title={Improved phenomenological renormalization schemes},
  author={M. A. Yurishchev},
  journal={Journal of Experimental and Theoretical Physics},
  year={2000},
  volume={91},
  pages={332-337}
}
  • M. Yurishchev
  • Published 1 August 2000
  • Physics
  • Journal of Experimental and Theoretical Physics
An analysis is made of various methods of phenomenological renormalization based on finite-dimensional scaling equations for inverse correlation lengths, the singular part of the free energy density, and their derivatives. The analysis is made using two-dimensional Ising and Potts lattices and the three-dimensional Ising model. Variants of equations for the phenomenological renormalization group are obtained which ensure more rapid convergence than the conventionally used Nightingale… 
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3 Citations

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TLDR
A simple criterion is found which allows for the straightforward determination of the order-disorder critical temperatures of the Ising model and predicts $\beta_c=0.2656...$ for the two coupled layers of Ising spins.
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