Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2
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Ilker-2014-Overfrustrated and underfrustrated.pdf
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1.08 MB
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Author(s)
Ilker, Efe
Berker, A. Nihat
Date Issued
April 2014
Journal
Physical Review E
Publisher
American Physical Society
Citation
Ilker, Efe, and A. Nihat Berker. “Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2.” Phys. Rev. E 89, no. 4 (April 2014). © 2014 American Physical Society
Version
Final published version
Abstract
In spin-glass systems, frustration can be adjusted continuously and considerably, without changing the antiferromagnetic bond probability p, by using locally correlated quenched randomness, as we demonstrate here on hypercubic lattices and hierarchical lattices. Such overfrustrated and underfrustrated Ising systems on hierarchical lattices in d = 3 and 2 are studied. With the removal of just 51% of frustration, a spin-glass phase occurs in d = 2. With the addition of just 33% frustration, the spin-glass phase disappears in d = 3. Sequences of 18 different phase diagrams for different levels of frustration are calculated in both dimensions. In general, frustration lowers the spin-glass ordering temperature. At low temperatures, increased frustration favors the spin-glass phase (before it disappears) over the ferromagnetic phase and symmetrically the antiferromagnetic phase. When any amount, including infinitesimal, frustration is introduced, the chaotic rescaling of local interactions occurs in the spin-glass phase. Chaos increases with increasing frustration, as can be seen from the increased positive value of the calculated Lyapunov exponent λ, starting from λ = 0 when frustration is absent. The calculated runaway exponent y[subscript R] of the renormalization-group flows decreases with increasing frustration to y[subscript R] = 0 when the spin-glass phase disappears. From our calculations of entropy and specific-heat curves in d = 3, it is shown that frustration lowers in temperature the onset of both long- and short-range order in spin-glass phases, but is more effective on the former. From calculations of the entropy as a function of antiferromagnetic bond concentration p, it is shown that the ground-state and low-temperature entropy already mostly sets in within the ferromagnetic and antiferromagnetic phases, before the spin-glass phase is reached.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.89.042139
