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arXiv · 1809.06029

A Lower Lower-Critical Spin-Glass Dimension from Quenched Mixed-Spatial-Dimensional Spin Glasses

Bora Atalay·A. Nihat Berker
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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_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_c, the spin-glass critical temperature continuously goes to zero, but the spin-glass chaos fully sustains 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_c and shows a discontinuity to zero at d_c.

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Bora Atalay, A. Nihat Berker. 2018-09-17. A Lower Lower-Critical Spin-Glass Dimension from Quenched Mixed-Spatial-Dimensional Spin Glasses. https://doi.org/10.1103/physreve.98.042125

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