IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v641y2024ics037843712400236x.html
   My bibliography  Save this article

Exact results for the Ising model on a small-world network

Author

Listed:
  • Ostilli, M.

Abstract

Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some kind of mean-field behavior. On the other hand, the links of the regular lattice make the system to retain some related non trivial correlations. The coexistence of these two features in general prevent a closed analytical treatment. Here we consider a one-dimensional small-world Ising model and derive analytically its equation of state, critical point, critical behavior, and critical correlations. Despite being one of the simplest small-world models, our exact and intuitive analysis reveals some intriguing properties.

Suggested Citation

  • Ostilli, M., 2024. "Exact results for the Ising model on a small-world network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    • Handle: RePEc:eee:phsmap:v:641:y:2024:i:c:s037843712400236x
    DOI: 10.1016/j.physa.2024.129727
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843712400236X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2024.129727?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ostilli, M., 2012. "Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(12), pages 3417-3423.
    2. M. Mézard & G. Parisi, 2001. "The Bethe lattice spin glass revisited," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(2), pages 217-233, March.
    3. A. Barrat & M. Weigt, 2000. "On the properties of small-world network models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 13(3), pages 547-560, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akın, Hasan, 2023. "The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Konstantinos Antoniadis & Kostas Zafiropoulos & Vasiliki Vrana, 2016. "A Method for Assessing the Performance of e-Government Twitter Accounts," Future Internet, MDPI, vol. 8(2), pages 1-18, April.
    3. Yue Chen & Xiaojian Niu & Yan Zhang, 2019. "Exploring Contrarian Degree in the Trading Behavior of China's Stock Market," Complexity, Hindawi, vol. 2019, pages 1-12, April.
    4. Lawford, Steve & Mehmeti, Yll, 2020. "Cliques and a new measure of clustering: With application to U.S. domestic airlines," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    5. Tsonis, Anastasios A. & Swanson, Kyle L. & Wang, Geli, 2008. "Estimating the clustering coefficient in scale-free networks on lattices with local spatial correlation structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5287-5294.
    6. Pollner, Péter & Palla, Gergely & Vicsek, Tamás, 2010. "Clustering of tag-induced subgraphs in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5887-5894.
    7. Ding Ding & Liyan Han & Libo Yin, 2017. "Systemic risk and dynamics of contagion: a duplex inter-bank network," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1435-1445, September.
    8. Elena Agliari & Adriano Barra & Andrea Galluzzi & Marco Alberto Javarone & Andrea Pizzoferrato & Daniele Tantari, 2015. "Emerging Heterogeneities in Italian Customs and Comparison with Nearby Countries," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-24, December.
    9. Hossein Sabzian & Mohammad Ali Shafia & Mehdi Ghazanfari & Ali Bonyadi Naeini, 2020. "Modeling the Adoption and Diffusion of Mobile Telecommunications Technologies in Iran: A Computational Approach Based on Agent-Based Modeling and Social Network Theory," Sustainability, MDPI, vol. 12(7), pages 1-36, April.
    10. Robson, Dominic T. & Annibale, Alessia & Baas, Andreas C.W., 2022. "Reproducing size distributions of swarms of barchan dunes on Mars and Earth using a mean-field model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    11. Robert Boyer & Denis Boyer & Gilles Laferté, 2007. "La connexion des réseaux comme facteur de changement institutionnel : l'exemple des vins de Bourgogne," PSE Working Papers halshs-00587708, HAL.
    12. Marr, Carsten & Hütt, Marc-Thorsten, 2005. "Topology regulates pattern formation capacity of binary cellular automata on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 641-662.
    13. Jie Yu & Fei You & Jian Wang & Zishan Wang, 2023. "Evolution Modes of Chili Pepper Industry Clusters under the Perspective of Social Network—An Example from Xinfu District, Xinzhou, Shanxi Province," Sustainability, MDPI, vol. 15(6), pages 1-14, March.
    14. Li, Chunguang, 2009. "Memorizing morph patterns in small-world neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 240-246.
    15. Jason Cory Brunson & Steve Fassino & Antonio McInnes & Monisha Narayan & Brianna Richardson & Christopher Franck & Patrick Ion & Reinhard Laubenbacher, 2014. "Evolutionary events in a mathematical sciences research collaboration network," Scientometrics, Springer;Akadémiai Kiadó, vol. 99(3), pages 973-998, June.
    16. Dassisti, M. & Carnimeo, L., 2013. "A small-world methodology of analysis of interchange energy-networks: The European behaviour in the economical crisis," Energy Policy, Elsevier, vol. 63(C), pages 887-899.
    17. Holme, Petter, 2007. "Scale-free networks with a large- to hypersmall-world transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 315-322.
    18. Wang, Xingyuan & Zhao, Tianfang & Qin, Xiaomeng, 2016. "Model of epidemic control based on quarantine and message delivery," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 168-178.
    19. Comellas, Francesc & Miralles, Alicia, 2009. "Modeling complex networks with self-similar outerplanar unclustered graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(11), pages 2227-2233.
    20. Konstantinos Petridis & Nikolaos E. Petridis, 2022. "Diffusion of Innovations in Middle Eastern versus Western Markets: A Mathematical Computation Cellular Automata Simulation Model," Operational Research, Springer, vol. 22(2), pages 1597-1616, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:641:y:2024:i:c:s037843712400236x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.