Lower-critical spin-glass dimension from 23 sequenced hierarchical models
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PhysRevE.92.022136.pdf
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156.32 KB
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Author(s)
Berker, A. Nihat
Demirtas, Mehmet
Tuncer, Asli
Date Issued
August 2015
Journal
Physical Review E
Publisher
American Physical Society
Citation
Demirtas, Mehmet, Asli Tuncer, and A. Nihat Berker. "Lower-critical spin-glass dimension from 23 sequenced hierarchical models." Phys. Rev. E 92, 022136 (August 2015). © 2015 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.92.022136
