On the discontinuity of the specific heat of the Ising model on a scale-free network
We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay P(K)∼ K-λ. It is well established that the model is characterized by classical mean-field exponents for λ > 5. In this note we show that the specific-heat discontinuity δ...
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| Published in: | Condensed Matter Physics |
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| Date: | 2015 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут фізики конденсованих систем НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155799 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | On the discontinuity of the specific heat of the Ising model on a scale-free network / M. Krasnytska, B. Berche, Yu. Holovatch, R. Kenna // Condensed Matter Physics. — 2015. — Т. 18, № 4. — С. 44601: 1–4. — Бібліогр.: 20 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862643120489889792 |
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| author | Krasnytska, M. Berche, B. Holovatch, Yu. Kenna, R. |
| author_facet | Krasnytska, M. Berche, B. Holovatch, Yu. Kenna, R. |
| citation_txt | On the discontinuity of the specific heat of the Ising model on a scale-free network / M. Krasnytska, B. Berche, Yu. Holovatch, R. Kenna // Condensed Matter Physics. — 2015. — Т. 18, № 4. — С. 44601: 1–4. — Бібліогр.: 20 назв. — англ. |
| collection | DSpace DC |
| container_title | Condensed Matter Physics |
| description | We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay P(K)∼ K-λ. It is well established that the model is characterized by classical mean-field exponents for λ > 5. In this note we show that the specific-heat discontinuity δc_h at the critical point remains λ-dependent even for λ > 5: δch=3(λ-5)(λ-1)/[2(λ-3)²] and attains its mean-field value δch=3/2 only in the limit λ → ∞. We compare this behaviour with recent measurements of the d dependency of δch made for the Ising model on lattices with d > 4 [Lundow P.H., Markström K., Nucl. Phys. B, 2015, 895, 305].
Ми розглядаємо модель Iзiнга на вiдпаленiй безмасштабнiй мережi зi степенево-спадною функцiєю розподiлу вузлiв P(K ) ∼ K
−λ. Вiдомо, що ця модель описується класичними критичними показниками середнього поля при λ > 5. Тут ми покажемо, що стрибок теплоємностi δch при критичнiй температурi залишається λ-залежним навiть для λ > 5: δch = 3(λ−5)(λ−1)/[2(λ−3)² ] i досягає свого середньопольового значення δch = 3/2 тiльки в границi λ → ∞. Ми порiвнюємо цю поведiнку iз недавнiми результатами залежностi δch вiд d для моделi Iзiнга на гратках з d > 4 [Lundow P.H., Markstr¨om K., Nucl. Phys. B, 2015,
895, 305].
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| first_indexed | 2025-12-01T07:31:35Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-155799 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-01T07:31:35Z |
| publishDate | 2015 |
| publisher | Інститут фізики конденсованих систем НАН України |
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| spelling | Krasnytska, M. Berche, B. Holovatch, Yu. Kenna, R. 2019-06-17T12:42:21Z 2019-06-17T12:42:21Z 2015 On the discontinuity of the specific heat of the Ising model on a scale-free network / M. Krasnytska, B. Berche, Yu. Holovatch, R. Kenna // Condensed Matter Physics. — 2015. — Т. 18, № 4. — С. 44601: 1–4. — Бібліогр.: 20 назв. — англ. 1607-324X PACS: 64.60.aq, 64.60.fd, 64.70.qd, 64.60.De DOI:10.5488/CMP.18.44601 arXiv:1510.06216 https://nasplib.isofts.kiev.ua/handle/123456789/155799 We consider the Ising model on an annealed scale-free network with node-degree distribution characterized by a power-law decay P(K)∼ K-λ. It is well established that the model is characterized by classical mean-field exponents for λ > 5. In this note we show that the specific-heat discontinuity δc_h at the critical point remains λ-dependent even for λ > 5: δch=3(λ-5)(λ-1)/[2(λ-3)²] and attains its mean-field value δch=3/2 only in the limit λ → ∞. We compare this behaviour with recent measurements of the d dependency of δch made for the Ising model on lattices with d > 4 [Lundow P.H., Markström K., Nucl. Phys. B, 2015, 895, 305]. Ми розглядаємо модель Iзiнга на вiдпаленiй безмасштабнiй мережi зi степенево-спадною функцiєю розподiлу вузлiв P(K ) ∼ K
 −λ. Вiдомо, що ця модель описується класичними критичними показниками середнього поля при λ > 5. Тут ми покажемо, що стрибок теплоємностi δch при критичнiй температурi залишається λ-залежним навiть для λ > 5: δch = 3(λ−5)(λ−1)/[2(λ−3)² ] i досягає свого середньопольового значення δch = 3/2 тiльки в границi λ → ∞. Ми порiвнюємо цю поведiнку iз недавнiми результатами залежностi δch вiд d для моделi Iзiнга на гратках з d > 4 [Lundow P.H., Markstr¨om K., Nucl. Phys. B, 2015,
 895, 305]. This work was supported in part by FP7 EU IRSES projects No. 295302 “Statistical Physics in Diverse
 Realizations”, No. 612707 “Dynamics of and in Complex Systems”, No. 612669 “Structure and Evolution
 of Complex Systems with Applications in Physics and Life Sciences”, and by the Doctoral College for the
 Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry (L
 4
 ). We thank Yuri Kozitsky for
 fruitful discussions. M.K. is grateful to Klas Markström for useful correspondence which initiated this
 study. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics On the discontinuity of the specific heat of the Ising model on a scale-free network Стрибок теплоємностi моделi Iзiнга на безмасштабнiй мережi Article published earlier |
| spellingShingle | On the discontinuity of the specific heat of the Ising model on a scale-free network Krasnytska, M. Berche, B. Holovatch, Yu. Kenna, R. |
| title | On the discontinuity of the specific heat of the Ising model on a scale-free network |
| title_alt | Стрибок теплоємностi моделi Iзiнга на безмасштабнiй мережi |
| title_full | On the discontinuity of the specific heat of the Ising model on a scale-free network |
| title_fullStr | On the discontinuity of the specific heat of the Ising model on a scale-free network |
| title_full_unstemmed | On the discontinuity of the specific heat of the Ising model on a scale-free network |
| title_short | On the discontinuity of the specific heat of the Ising model on a scale-free network |
| title_sort | on the discontinuity of the specific heat of the ising model on a scale-free network |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155799 |
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