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

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

PHYSICAL REVIEW E, vol.92, no.2, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 92 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1103/physreve.92.022136
  • Title of Journal : PHYSICAL REVIEW E


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.