Lower-critical spin-glass dimension from 23 sequenced hierarchical models

Demirtas M., Tuncer A., Berker A. N.

PHYSICAL REVIEW E, cilt.92, sa.2, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 92 Sayı: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1103/physreve.92.022136
  • Dergi Adı: PHYSICAL REVIEW E
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • İstanbul Teknik Üniversitesi Adresli: Evet

Özet

The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as d(L) = 2.520 for a family of hierarchical lattices, from an essentially exact (correlation coefficent R-2 = 0.999 999) near-linear fit to 23 different diminishing fractional dimensions. To obtain this result, the phase transition temperature between the disordered and spin-glass phases, the corresponding critical exponent y(T), and the runaway exponent y(R) of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered.