Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering
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 hiera...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/115320 https://orcid.org/0000-0002-5172-2172 |
| _version_ | 1811080081172332544 |
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| author | Atalay, Bora Berker, A Nihat |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Atalay, Bora Berker, A Nihat |
| author_sort | Atalay, Bora |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:25:31Z |
| format | Article |
| id | mit-1721.1/115320 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:25:31Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1153202022-10-01T03:30:46Z Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering Atalay, Bora Berker, A Nihat Massachusetts Institute of Technology. Department of Physics Berker, A Nihat 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. 2018-05-11T15:19:04Z 2018-05-11T15:19:04Z 2018-05 2018-01 2018-05-02T18:00:17Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/115320 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 https://orcid.org/0000-0002-5172-2172 en http://dx.doi.org/10.1103/PhysRevE.97.052102 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Atalay, Bora Berker, A Nihat Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| title | Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| title_full | Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| title_fullStr | Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| title_full_unstemmed | Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| title_short | Maximally random discrete-spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| title_sort | maximally random discrete spin systems with symmetric and asymmetric interactions and maximally degenerate ordering |
| url | http://hdl.handle.net/1721.1/115320 https://orcid.org/0000-0002-5172-2172 |
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