A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa'
It is well known that standard hyperscaling breaks down above the upper critical dimension dc, where the critical exponents take on their Landau values. Here we show that this is because, in standard formulations in the thermodynamic limit, distance is measured on the correlation-length scale. Howev...
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| Видавець: | Інститут фізики конденсованих систем НАН України |
|---|---|
| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2013
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/120813 |
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| Цитувати: | A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' / R. Kenna, B. Berche// Condensed Matter Physics. — 2013. — Т. 16, № 2. — С. 23601:1-12. — Бібліогр.: 46 назв. — англ. |
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irk-123456789-1208132017-06-14T03:02:51Z A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' Kenna, R. Berche, B. It is well known that standard hyperscaling breaks down above the upper critical dimension dc, where the critical exponents take on their Landau values. Here we show that this is because, in standard formulations in the thermodynamic limit, distance is measured on the correlation-length scale. However, the correlation-length scale and the underlying length scale of the system are not the same at or above the upper critical dimension. Above dc they are related algebraically through a new critical exponent \coppa, while at dc they differ through logarithmic corrections governed by an exponent \hat{\coppa}. Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions. Вiдомо, що стандартний гiперскейлiнг порушується вище верхньої критичної вимiрностi dc, де критичнi показники приймають класичнi значення. Тут ми показуємо, що це є тому, що в стандартних формулюваннях у термодинамiчнiй границi вiдстань вимiрюється на масштабах кореляцiйної довжини. Проте, масштаб кореляцiйної довжини i власний масштаб довжини системи не є однаковi бiля чи вище вищої критичної вимiрностi. Вище dc вони пов’язанi алгебраїчно через новий критичний показник, тодi як бiля dc вони рiзняться на логарифмiчнi поправки, що керуються показником . Врахування належним чином цих рiзних масштабiв довжини дозволяє розширити гiперскейлiнг до всiх вимiрностей. 2013 Article A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' / R. Kenna, B. Berche// Condensed Matter Physics. — 2013. — Т. 16, № 2. — С. 23601:1-12. — Бібліогр.: 46 назв. — англ. 1607-324X PACS: 64.60.-i,64.60.an,05.50.+q,64.60.De,11.10.Kk DOI:10.5488/CMP.16.23601 http://dspace.nbuv.gov.ua/handle/123456789/120813 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 |
It is well known that standard hyperscaling breaks down above the upper critical dimension dc, where the critical exponents take on their Landau values. Here we show that this is because, in standard formulations in the thermodynamic limit, distance is measured on the correlation-length scale. However, the correlation-length scale and the underlying length scale of the system are not the same at or above the upper critical dimension. Above dc they are related algebraically through a new critical exponent \coppa, while at dc they differ through logarithmic corrections governed by an exponent \hat{\coppa}. Taking proper account of these different length scales allows one to extend hyperscaling to all dimensions. |
| format |
Article |
| author |
Kenna, R. Berche, B. |
| spellingShingle |
Kenna, R. Berche, B. A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' Condensed Matter Physics |
| author_facet |
Kenna, R. Berche, B. |
| author_sort |
Kenna, R. |
| title |
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' |
| title_short |
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' |
| title_full |
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' |
| title_fullStr |
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' |
| title_full_unstemmed |
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' |
| title_sort |
new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120813 |
| citation_txt |
A new critical exponent 'coppa' and its logarithmic counterpart 'hat coppa' / R. Kenna, B. Berche// Condensed Matter Physics. — 2013. — Т. 16, № 2. — С. 23601:1-12. — Бібліогр.: 46 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-10-18T20:38:02Z |
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2023-10-18T20:38:02Z |
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