Lower lower-critical spin-glass dimension from quenched mixed-spatial-dimensional spin glasses
Name
PhysRevE.98.042125.pdf
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1006.33 KB
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Adobe PDF
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9e79dc96441566f8c870a67e4051043c
Author(s)
Atalay, Bora
Berker, A Nihat
Date Issued
October 2018
Journal
Physical Review E
Publisher
American Physical Society
Citation
Atalay, Bora, and A. Nihat Berker. “Lower Lower-Critical Spin-Glass Dimension from Quenched Mixed-Spatial-Dimensional Spin Glasses.” Physical Review E, vol. 98, no. 4, Oct. 2018. © 2018 American Physical Society
Version
Final published version
Abstract
By quenched-randomly mixing local units of different spatial dimensionalities, we have studied Ising spin-glass systems on hierarchical lattices continuously in dimensionalities 1≤d≤3. The global phase diagram in temperature, antiferromagnetic bond concentration, and spatial dimensionality is calculated. We find that, as dimension is lowered, the spin-glass phase disappears to zero temperature at the lower-critical dimension d[subscript c]=2.431. Our system being a physically realizable system, this sets an upper limit to the lower-critical dimension in general for the Ising spin-glass phase. As dimension is lowered towards d[subscript c], the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully subsists to the brink of the disappearance of the spin-glass phase. The Lyapunov exponent, measuring the strength of chaos, is thus largely unaffected by the approach to d[subscript c}] and shows a discontinuity to zero at d[subscript c].
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.98.042125
