Stability of the Griffiths phase in a 2D Potts model with correlated disorder
A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D q-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, onl...
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| Дата: | 2014 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2014
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/153557 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Stability of the Griffiths phase in a 2D Potts model with correlated disorder / C. Chatelain // Condensed Matter Physics. — 2014. — Т. 17, № 3. — С. 33601:1-11. — Бібліогр.: 23 назв. — англ. |
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irk-123456789-1535572019-06-15T01:25:34Z Stability of the Griffiths phase in a 2D Potts model with correlated disorder Chatelain, C. A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D q-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, only relatively small lattice sizes could be considered, so one can wonder whether this Griffiths phase will not shrink and collapse into a single point, the critical point, as the lattice size is increased to much larger values. In this paper, the 2D eight-state Potts model is numerically studied for four different disorder correlations. It is shown that the Griffiths phase cannot be explained as a simple spreading of local transition temperatures caused by disorder fluctuations. As a consequence, the vanishing of the latter in the thermodynamic limit does not necessarily imply the collapse of the Griffiths phase into a single point. By contrast, the width of the Griffiths phase is controlled by the disorder strength. However, for disorder correlations decaying slower than 1/r, no cross-over to a more usual critical behavior could be observed as this strength is tuned to weaker values. Використовуючи метод Монте Карло, недавно отримано фазу Грiффiтса у двовимiрний q-становiй моделi Поттса з сильно скорельованими замороженими хаточними зв’язками. Зокрема, показано, що магнiтна сприйнятливiсть розбiгається алгебраїчно з розмiром гратки в широкому iнтервалi температур. Оскiльки тiльки вiдносно малi розмiри граток можуть розглядатися, цiкаво дiзнатися, чи ця фаза Грiффiтса не стягується i колапсує в одну точку, критичну точку, якщо розмiр гратки стає набагато бiльшим. В цiй статтi, двовимiрна восьмистанова модель Поттса вивчається чисельно для чотирьох рiзних кореляцiй. Показано, що фазу Грiффiтса не можна пояснити як просте поширення локальних температур переходу, спричинених флуктуацiями безладу. Як наслiдок, зникнення останнього в термодинамiчний границi не обов’язково означає колапс фази Грiффiтса в одну точку. На вiдмiну вiд цього, ширина фази Грiффiтса контролюється силою безладу. Проте, для кореляцiй безладу, що згасають повiльнiше нiж 1/r , жодний кросовер до бiльш звичайної критичної поведiнки не мав би спостерiгатись, якщо ця сила зменшується до певного значення. 2014 Article Stability of the Griffiths phase in a 2D Potts model with correlated disorder / C. Chatelain // Condensed Matter Physics. — 2014. — Т. 17, № 3. — С. 33601:1-11. — Бібліогр.: 23 назв. — англ. 1607-324X DOI:10.5488/CMP.17.33601 PACS: 64.60.De, 05.50.+q, 05.70.Jk, 05.10.Ln arXiv:1404.6431 http://dspace.nbuv.gov.ua/handle/123456789/153557 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D q-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, only relatively small lattice sizes could be considered, so one can wonder whether this Griffiths phase will not shrink and collapse into a single point, the critical point, as the lattice size is increased to much larger values. In this paper, the 2D eight-state Potts model is numerically studied for four different disorder correlations. It is shown that the Griffiths phase cannot be explained as a simple spreading of local transition temperatures caused by disorder fluctuations. As a consequence, the vanishing of the latter in the thermodynamic limit does not necessarily imply the collapse of the Griffiths phase into a single point. By contrast, the width of the Griffiths phase is controlled by the disorder strength. However, for disorder correlations decaying slower than 1/r, no cross-over to a more usual critical behavior could be observed as this strength is tuned to weaker values. |
| format |
Article |
| author |
Chatelain, C. |
| spellingShingle |
Chatelain, C. Stability of the Griffiths phase in a 2D Potts model with correlated disorder Condensed Matter Physics |
| author_facet |
Chatelain, C. |
| author_sort |
Chatelain, C. |
| title |
Stability of the Griffiths phase in a 2D Potts model with correlated disorder |
| title_short |
Stability of the Griffiths phase in a 2D Potts model with correlated disorder |
| title_full |
Stability of the Griffiths phase in a 2D Potts model with correlated disorder |
| title_fullStr |
Stability of the Griffiths phase in a 2D Potts model with correlated disorder |
| title_full_unstemmed |
Stability of the Griffiths phase in a 2D Potts model with correlated disorder |
| title_sort |
stability of the griffiths phase in a 2d potts model with correlated disorder |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2014 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/153557 |
| citation_txt |
Stability of the Griffiths phase in a 2D Potts model with correlated disorder / C. Chatelain // Condensed Matter Physics. — 2014. — Т. 17, № 3. — С. 33601:1-11. — Бібліогр.: 23 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-05-20T17:39:57Z |
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2023-05-20T17:39:57Z |
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1796153802721591296 |