Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models

Mehmet Demirtas; Asli Tuncer; A. Nihat Berker

doi:10.1103/physreve.92.022136

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arXiv · 1502.06443

Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models

Mehmet Demirtas·Asli Tuncer·A. Nihat Berker

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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.

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Mehmet Demirtas, Asli Tuncer, A. Nihat Berker. 2015-02-23. Lower-Critical Spin-Glass Dimension from 23 Sequenced Hierarchical Models. https://doi.org/10.1103/physreve.92.022136

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