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 $d_L=2.520$ for a family of hierarchical lattices, from an essentially exact (correlation coefficent $R^2=0.999999$) 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 $y_T$, and the runaway exponent $y_R$ of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered.

5 pages, 2 figures, 1 table

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• Axial, Planar-Diagonal, Body-Diagonal Fields on the Cubic-Spin Spin Glass in d=3: A Plethora of Ordered Phases under Finite Fields