https://doi.org/10.1140/epjb/s10051-025-01060-8
Research - Statistical and Nonlinear Physics
Mean-field theory of the general-spin Ising model
University of Amsterdam, Nieuwe Achtergracht 129-B, 1018 NP, Amsterdam, The Netherlands
Received:
19
May
2025
Accepted:
17
September
2025
Published online:
15
October
2025
Motivated by modelling in physics and other disciplines, such as sociology and psychology, we derive the mean field of the general-spin Ising model from the variational principle of the Gibbs free energy. The general-spin Ising model has 
spin values, generated by 
, with 
, such that for 
we obtain 
, for example; the Hamiltonian is identical to that of the standard Ising model. The general-spin Ising model exhibits spontaneous magnetisation, similar to the standard Ising model, but with the location translated by a factor depending on the number of categories . We also show how the accuracy of the mean field depends on both the number of nodes and node degree, and that the hysteresis effect decreases and saturates with the number of categories . Monte Carlo simulations confirm the theoretical results.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
