General Features of the q-XY Opinion Model

Dode Prenga


In this article, we will discuss the general properties of the q-opinion model, which is based on the extension of the XY magnet model. After considering a short briefing of our recently introduced q-XY model and providing the general statistical mechanics calculation for it, we analysed the specifics and application of the 2-node chain. The model is capable of interpreting some particular features of the opinions of a couple, including shifting behavior, losing interest in a given issue for specific opinion microstates, etc. We proposed to use this model in a modified version of the preferential attachment rule for link establishment in a social network.


Doi: 10.28991/HEF-2020-01-02-05

Full Text: PDF


Opinion Dynamics; XY Magnets; q-XY Opinion; Statistical Mechanics.


Holley, R. A., & Liggett, T. M. (1975). Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model. The Annals of Probability, 3(4). doi:10.1214/aop/1176996306.

Clifford, P., & Sudbury, A. (1973). A model for spatial conflict. Biometrika, 60(3), 581–588. doi:10.1093/biomet/60.3.581.

Potts, R. B. (1952). Some generalized order-disorder transformations. Mathematical Proceedings of the Cambridge Philosophical Society, 48(1), 106–109. doi:10.1017/s0305004100027419.

Stauffer, D. (2012). A Biased Review of Sociophysics. Journal of Statistical Physics, 151(1-2), 9–20. doi:10.1007/s10955-012-0604-9.

Albert, R., & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47–97. doi:10.1103/revmodphys.74.47.

Dorogovtsev, S. N., Mendes, J. F. F., & Samukhin, A. N. (2000). Structure of Growing Networks with Preferential Linking. Physical Review Letters, 85(21), 4633–4636. doi:10.1103/physrevlett.85.4633.

Barabási, A.-L. (2013). Network science. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1987), 20120375. doi:10.1098/rsta.2012.0375.

Castellano, C., Fortunato, S., & Loreto, V. (2009). Statistical physics of social dynamics. Reviews of Modern Physics, 81(2), 591–646. doi:10.1103/revmodphys.81.591.

Albi, G., Pareschi, L., & Zanella, M. (2016). Opinion dynamics over complex networks: Kinetic modelling and numerical methods. American Institute of Mathematical Sciences, 10(1): 1-32.

Redner, S. (2019). Reality-inspired voter models: A mini-review. Comptes Rendus Physique, 20(4), 275–292. doi:10.1016/j.crhy.2019.05.004.

Kou, G., Zhao, Y., Peng, Y., & Shi, Y. (2012). Multi-Level Opinion Dynamics under Bounded Confidence. PLoS ONE, 7(9), e43507. doi:10.1371/journal.pone.0043507.

Deffuant, G., Neau, D., Amblard, F., & Weisbuch, G. (2000). Mixing beliefs among interacting agents. Advances in Complex Systems, 03(01n04), 87–98. doi:10.1142/s0219525900000078.

Hegselmann, R., & Krause, U. (2002). Opinion dynamics and bounded confidence models, analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3), 1-33.

Lorenz, J. (2007). Continuous Opinion Dynamics under Bounded Confidence: A Survey. International Journal of Modern Physics C, 18(12), 1819–1838. doi:10.1142/s0129183107011789.

Flache, A., & Hegselmann, R. (2001). Do irregular grids make a difference? Relaxing the spatial regularity assumption in cellular models of social dynamics. Journal of Artificial Societies and Social Simulation, 4(4), 1-12.

Ciftja, O., & Prenga, D. (2016). Magnetic properties of a classical XY spin dimer in a “planar” magnetic field. Journal of Magnetism and Magnetic Materials, 416, 220–225. doi:10.1016/j.jmmm.2016.04.070.

Ciftja, O., Luban, M., Auslender, M., & Luscombe, J. H. (1999). Equation of state and spin-correlation functions of ultrasmall classical Heisenberg magnets. Physical Review B, 60(14), 10122–10133. doi:10.1103/physrevb.60.10122.

Ciftja, O. (2007). Spin dynamics of an ultra-small nanoscale molecular magnet. Nanoscale Research Letters, 2(3), 1-7. doi:10.1007/s11671-007-9049-5.

Noorazar, H., Sottile, M. J., & Vixie, K. R. (2018). An energy-based interaction model for population opinion dynamics with topic coupling. International Journal of Modern Physics C, 29(11), 1850115. doi:10.1142/s0129183118501152.

Prenga, D., Kushta, E., & Ifti, M. (2020). Modelling militantism and partisanship spread in the chain and square lattice opinion structures by using q-XY opinion model. Journal of Physics: Conference Series, 1730(1), 012087. doi:10.1088/1742-6596/1730/1/012087.

Galam, S., Gefen (Feigenblat), Y., & Shapir, Y. (1982). Sociophysics: A new approach of sociological collective behaviour. I. mean-behaviour description of a strike. The Journal of Mathematical Sociology, 9(1), 1-13. doi:10.1080/0022250x.1982.9989929.

Prenga, D. (2019). A two-stage opinion formation model based on the extended XY-magnet interaction and socio-dynamic update mechanism. Journal of Physics: Conference Series, 1391, 012056. doi:10.1088/1742-6596/1391/1/012056.

Prenga, D., & Ifti, M. (2012). Distribution of Votes and a Model of Political Opinion Formation for Majority Elections. International Journal of Modern Physics: Conference Series, 16, 1–12. doi:10.1142/s2010194512007738.

Leoncini, X., Verga, A. D., & Ruffo, S. (1998). Hamiltonian dynamics and the phase transition of theXYmodel. Physical Review E, 57(6), 6377–6389. doi:10.1103/physreve.57.6377.

Schweitzer, F., Krivachy, T., & Garcia, D. (2020). An Agent-Based Model of Opinion Polarization Driven by Emotions. Complexity, 2020, 1–11. doi:10.1155/2020/5282035.

Full Text: PDF

DOI: 10.28991/HEF-2020-01-02-05


  • There are currently no refbacks.

Copyright (c) 2021 Dode Prenga