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

Abstract

The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as d[subscript L] = 2.520 for a family of hierarchical lattices, from an essentially exact (correlation coefficent R[superscript 2] = 0.999999) 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[subscript T], and the runaway exponent y[subscript R] of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered.