Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering
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PhysRevE.97.052102.pdf
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Author(s)
Atalay, Bora
Berker, A Nihat
Date Issued
May 2018
Journal
Physical Review E
Publisher
American Physical Society
Citation
Atalay, Bora and Berker, A. Nihat. "Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering." Physical Review E 97, 5 (May 2018): 052102 © 2018 American Physical Society
Version
Final published version
Abstract
Discrete-spin systems with maximally random nearest-neighbor interactions that can be symmetric or asymmetric, ferromagnetic or antiferromagnetic, including off-diagonal disorder, are studied, for the number of states q=3,4 in d dimensions. We use renormalization-group theory that is exact for hierarchical lattices and approximate (Migdal-Kadanoff) for hypercubic lattices. For all d>1 and all noninfinite temperatures, the system eventually renormalizes to a random single state, thus signaling q×q degenerate ordering. Note that this is the maximally degenerate ordering. For high-temperature initial conditions, the system crosses over to this highly degenerate ordering only after spending many renormalization-group iterations near the disordered (infinite-temperature) fixed point. Thus, a temperature range of short-range disorder in the presence of long-range order is identified, as previously seen in underfrustrated Ising spin-glass systems. The entropy is calculated for all temperatures, behaves similarly for ferromagnetic and antiferromagnetic interactions, and shows a derivative maximum at the short-range disordering temperature. With a sharp immediate contrast of infinitesimally higher dimension 1+ε, the system is as expected disordered at all temperatures for d=1.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevE.97.052102
