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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References

SHOWING 1-10 OF 27 REFERENCES
Finite‐size scaling and phenomenological renormalization (invited)
Research in recent years has shown that combining finite‐size scaling theory with the transfer matrix technique yields a powerful tool for the investigation of critical behavior. In particular, the
Critical finite-size-scaling amplitudes of a fully anisotropic three-dimensional Ising model
A fully anisotropic simple-cubic Ising lattice in the geometry of periodic cylinders n{times}n{times}{infinity} is investigated by the transfer-matrix finite-size-scaling method. In addition to the
Phenomenological scaling approach to the triangular Ising antiferromagnet
We apply the phenomenological scaling approach of Nightingale to the triangular Ising model with nearest-neighbor interactions in the presence of a magnetic field. In order to do so, we calculate the
Hyperuniversality of a fully anisotropic three-dimensional Ising model.
  • Yurishchev
  • Physics
    Physical review. B, Condensed matter
  • 1994
For the fully anisotropic simple-cubic Ising lattice, the critical finite-size scaling amplitudes of both the spin-spin and energy-energy inverse correlation lengths and the singular part of the
Locating analytically critical temperatures in some statistical systems.
  • Wosiek
  • Physics
    Physical review. B, Condensed matter
  • 1994
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.
Finite size scaling analysis of ising model block distribution functions
The distribution functionPL(s) of the local order parameters in finite blocks of linear dimensionL is studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is
and from 3D Ising energy and specific heat
We analyse Monte Carlo data for the energy and specific heat at and close to the critical point of the 3D cubic Ising model. From the finite-size scaling of the energy E and the specific heat C at
Universal critical amplitudes in finite-size scaling
It is argued that there is no nonuniversal, system-dependent, multiplicative metric factor in the finite-size scaling relation for the singular part of the free energy near a bulk critical point. New
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