Revisiting (logarithmic) scaling relations using renormalization group
We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper critical behavior (for short and long range φ n -theories) an...
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| Date: | 2017 |
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| Language: | English |
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Інститут фізики конденсованих систем НАН України
2017
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| Series: | Condensed Matter Physics |
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| Cite this: | Revisiting (logarithmic) scaling relations using renormalization group / J.J. Ruiz-Lorenzo // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13601: 1–10. — Бібліогр.: 25 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-1565472025-02-23T17:16:58Z Revisiting (logarithmic) scaling relations using renormalization group Перегляд (логарифмiчних) спiввiдношень скейлiнгу з використанням ренормгрупи Ruiz-Lorenzo, J.J. We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper critical behavior (for short and long range φ n -theories) and below it. This allows us to check the scaling relations among these critical exponents obtained by analysing the complex singularities (Lee-Yang and Fisher zeroes) of these models. Moreover, we have obtained an explicit method to compute the ϙˆ exponent [defined by ξ ∼ L(logL) ϙˆ ] and, finally, we have found a new derivation of the scaling law associated with it. Ми явно обчислюємо критичнi показники, пов’язанi з логарифмiчними поправками, виходячи з рiвнянь ренормгрупи i середньопольової поведiнки для широкого класу моделей як при вищiй критичнiй вимiрностi (для коротко- i далекосяжних φ n -теорiй), так i нижче вiд неї. Це дозволяє нам перевiрити спiввiдношення скейлiнгу, що пов’язують критичнi показники, аналiзуючи комплекснi сингулярностi (нулi Лi-Янга i Фiшера) цих моделей. Окрiм того, ми запропонували явний метод для обчислення показника ϙˆ [означеного як ξ ∼ L(logL) ϙˆ ] i, накiнець, ми отримали нове виведення закона скейлiнгу, пов’язаного з цим показником. I dedicate this paper to Y. Holovatch to celebrate his 60th birthday. I acknowledge interesting discussions with R. Kenna, B. Berche and M. Dudka. This work was partially supported by Ministerio de Economía y Competitividad (Spain) through Grants No. FIS2013-42840-P and FIS2016-76359-P (partially funded by FEDER) and by Junta de Extremadura (Spain) through Grant No. GRU10158 (partially funded by FEDER). 2017 Article Revisiting (logarithmic) scaling relations using renormalization group / J.J. Ruiz-Lorenzo // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13601: 1–10. — Бібліогр.: 25 назв. — англ. 1607-324X PACS: 64.60-j,05.50+q,05.70.Jk,75.10.Hk DOI:10.5488/CMP.20.13601 arXiv:1702.05072 https://nasplib.isofts.kiev.ua/handle/123456789/156547 en Condensed Matter Physics application/pdf Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models
at the upper critical behavior (for short and long range φ
n
-theories) and below it. This allows us to check the
scaling relations among these critical exponents obtained by analysing the complex singularities (Lee-Yang and
Fisher zeroes) of these models. Moreover, we have obtained an explicit method to compute the ϙˆ exponent
[defined by ξ ∼ L(logL)
ϙˆ
] and, finally, we have found a new derivation of the scaling law associated with it. |
| format |
Article |
| author |
Ruiz-Lorenzo, J.J. |
| spellingShingle |
Ruiz-Lorenzo, J.J. Revisiting (logarithmic) scaling relations using renormalization group Condensed Matter Physics |
| author_facet |
Ruiz-Lorenzo, J.J. |
| author_sort |
Ruiz-Lorenzo, J.J. |
| title |
Revisiting (logarithmic) scaling relations using renormalization group |
| title_short |
Revisiting (logarithmic) scaling relations using renormalization group |
| title_full |
Revisiting (logarithmic) scaling relations using renormalization group |
| title_fullStr |
Revisiting (logarithmic) scaling relations using renormalization group |
| title_full_unstemmed |
Revisiting (logarithmic) scaling relations using renormalization group |
| title_sort |
revisiting (logarithmic) scaling relations using renormalization group |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2017 |
| citation_txt |
Revisiting (logarithmic) scaling relations using renormalization group / J.J. Ruiz-Lorenzo // Condensed Matter Physics. — 2017. — Т. 20, № 1. — С. 13601: 1–10. — Бібліогр.: 25 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT ruizlorenzojj revisitinglogarithmicscalingrelationsusingrenormalizationgroup AT ruizlorenzojj pereglâdlogarifmičnihspivvidnošenʹskejlinguzvikoristannâmrenormgrupi |
| first_indexed |
2025-07-22T04:13:38Z |
| last_indexed |
2025-07-22T04:13:38Z |
| _version_ |
1838319003590721536 |