The 2D non self-dual Ising lattices: An exact renormalization group treatment

KAYA T.

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, cilt.35, sa.13, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 35 Sayı: 13
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s0217979221501708
  • Dergi Adı: INTERNATIONAL JOURNAL OF MODERN PHYSICS B
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Ising model, renormalization group, phase transition and critical phenomena, CRYSTAL STATISTICS, MODEL, GRAPHENE, EQUATIONS, ORDER
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this work, an exact renormalization group treatment of honeycomb lattice leading to an exact relation between the coupling strengths of the honeycomb and the triangular lattices is presented. Using the honeycomb and the triangular duality relation, the critical coupling values of honeycomb and triangular lattices are calculated exactly by the simultaneous solution of the renormalized relation and the duality relation, without using the so-called star-triangular transformation. Apparently, the obtained coupling relation is unique. It not only takes place the role of the star triangular relation, but it is also the only exact relation obtained from renormalization group theory other than the 1D Ising chain. An exact pair correlation function expression relating the nearest neighbors and the next nearest neighbor correlation functions are also obtained for the honeycomb lattice. Utilizing this correlation relation, an exact expression of the correlation length of the honeycomb lattice is calculated analytically for the coupling constant values less than the critical value in the realm of the scaling theory. The critical exponents nu and alpha are also calculated as nu = 1 and alpha = 0.