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Current issue   Ukr. J. Phys. 2015, Vol. 59, N 7, p.655-662
https://doi.org/10.15407/ujpe59.07.0655    Paper

Borisenko O., Chelnokov V., Kushnir V.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03143, Ukraine;
e-mail: oleg@bitp.kiev.ua, chelnokov@bitp.kiev.ua. vkushnir@bitp.kiev.ua)

Phenomenological Renormalization Group and Cluster Approximation

Section: Fields and elementary particles
Original Author's Text: English

Abstract: We propose a modification of the Nightingale renormalization group for lattice spin and gauge models by combining it with the cluster decimation approximation. Essential ingredients of our approach are: 1) exact calculation of the partition and correlation functions on a finite lattice strip; 2) preservation of the mass gap or the second moment correlation length, computed in the infinite strip length limit, on each decimation step. The method is applied to studying the general two- and three-dimensional Z(N) models. A perfect agreement with exact results (whenever available) is found. An extension of the method to models with a continuous symmetry is briefly discussed.

Key words: phenomenological renormalization group, transfer matrix, Potts model.


  1. A.A. Migdal, Sov. Phys.-JETP 42, 743 (1975).
  2. L.P. Kadanoff, Ann. Phys. 100, 359 (1976).
  3. K.R. Ito, Phys. Rev. Lett. 54, 2383 (1985);
    Phys.Rev.Lett. 55, 558 (1985).
  4. R.E. Goldstein and J.S. Walker, J. Phys. A: Math. Gen. 18, 1275 (1985).
  5. M.P. Nightingale, Physica 83A, 561 (1976).
  6. M.P. Nightingale, J. Appl. Phys. 53, 7927 (1982).
  7. M.A. Yurishchev, JETP 91, 332 (2000).
  8. F.J. Wu, Rev. Mod. Phys. 54, 235 (1982).
  9. Jesus Salas, Shu-Chiuan Chang, and Robert Shrock, J. Stat. Phys. 107, 1207 (2002).
  10. A. Bazavov, B.A. Berg, and S. Dubey, Nucl. Phys. B 802, 421 (2008).
  11. O. Borisenko, V. Chelnokov, G. Cortese, M. Gravina, A. Papa, and I. Surzhikov, Nucl. Phys. B 873, 80 (2014).
  12. M. Caselle, A. Feo, M. Panero, and R. Pellegrini, JHEP 2011:020 (2011).