title: 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 dL=2.520 for a family of hierarchical lattices, from an essentially exact (correlation coefficent R2=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 yT, and the runaway exponent yR of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered.
authors.affiliation: Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, Istanbul, Turkey.
authors.forename: Mehmet
authors.initials: M
authors.lastname: Demirtaş
authors.affiliation: Department of Physics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey.
authors.forename: Aslı
authors.initials: A
authors.lastname: Tuncer
authors.affiliation: Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, Istanbul, Turkey.|Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: A Nihat
authors.initials: AN
authors.lastname: Berker