Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2
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 underfrustrat...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2014
|
| Online Access: | http://hdl.handle.net/1721.1/89023 https://orcid.org/0000-0002-5172-2172 |
| _version_ | 1826199623751958528 |
|---|---|
| author | Ilker, Efe Berker, A. Nihat |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Ilker, Efe Berker, A. Nihat |
| author_sort | Ilker, Efe |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:23:13Z |
| format | Article |
| id | mit-1721.1/89023 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:23:13Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/890232022-09-27T19:10:25Z Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 Ilker, Efe Berker, A. Nihat Massachusetts Institute of Technology. Department of Physics Berker, A. Nihat 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. 2014-08-25T15:40:06Z 2014-08-25T15:40:06Z 2014-04 2013-11 Article http://purl.org/eprint/type/JournalArticle 1539-3755 1550-2376 http://hdl.handle.net/1721.1/89023 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 https://orcid.org/0000-0002-5172-2172 en_US http://dx.doi.org/10.1103/PhysRevE.89.042139 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. application/pdf American Physical Society American Physical Society |
| spellingShingle | Ilker, Efe Berker, A. Nihat Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 |
| title | Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 |
| title_full | Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 |
| title_fullStr | Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 |
| title_full_unstemmed | Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 |
| title_short | Overfrustrated and Underfrustrated Spin Glasses in d = 3 and 2: Evolution of Phase Diagrams and Chaos Including Spin-Glass Order in d = 2 |
| title_sort | overfrustrated and underfrustrated spin glasses in d 3 and 2 evolution of phase diagrams and chaos including spin glass order in d 2 |
| url | http://hdl.handle.net/1721.1/89023 https://orcid.org/0000-0002-5172-2172 |
| work_keys_str_mv | AT ilkerefe overfrustratedandunderfrustratedspinglassesind3and2evolutionofphasediagramsandchaosincludingspinglassorderind2 AT berkeranihat overfrustratedandunderfrustratedspinglassesind3and2evolutionofphasediagramsandchaosincludingspinglassorderind2 |