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(in progress) I present several ising-like models used in many fields of science.
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(in progress) a list of applications of the Ising model and Ising-like models

  • 01-Social dynamics:
  • 02-Economy and Finance
  • 03-Biology
  • 04-Neuroscience
  • 05-Complex Systems & General Things
  • 06-Wetting
  • 07-Casimir effects
  • 08-Geophysics
  • 09-Models inspired by the Ising model
  • 10-History of the model

1-Social dynamics:

  • Stauffer, Dietrich. "Social applications of two-dimensional Ising models." American Journal of Physics 76.4 (2008): 470-473.
  • Galam, Serge. "Rational group decision making: A random field Ising model at T= 0." Physica A: Statistical Mechanics and its Applications 238.1 (1997): 66-80.
  • Laciana, Carlos E., and Santiago L. Rovere. "Ising-like agent-based technology diffusion model: Adoption patterns vs. seeding strategies." Physica A: Statistical Mechanics and its Applications 390.6 (2011): 1139-1149.
  • "Ising-based model of opinion formation in a complex network of interpersonal interactions." Physica A: Statistical Mechanics and its Applications 361.2 (2006): 651-664.
  • Dasgupta, Subinay, Raj Kumar Pan, and Sitabhra Sinha. "Phase of Ising spins on modular networks analogous to social polarization." Physical Review E 80.2 (2009): 025101.
  • del Río, Ana Fernández. "Coupled Ising models and interdependent discrete choices under social influence in homogeneous populations." arXiv preprint arXiv:1104.4887 (2011).
  • Lee, Edward D., William Bialek, and Ned Wingreen. "Investigating Correlations in the US Supreme Court with the Ising Model." (2011).
  • Lucena Júnior, José Emílio de. Modelo de Ising aplicado ao estudo da criminalidade. Diss. Universidade de São Paulo.
  • Stauffer, Dietrich, and Sorin Solomon. "Ising, Schelling and self-organising segregation." The European Physical Journal B 57.4 (2007): 473-479.
  • Ódor, Géza. "Self-organizing, two-temperature Ising model describing human segregation." International journal of modern physics C 19.03 (2008): 393-398.
  • Müller, Katharina, Christian Schulze, and Dietrich Stauffer. "Inhomogeneous and self-organized temperature in Schelling-Ising model." International Journal of Modern Physics C 19.03 (2008): 385-391.
  • Sumour, M. A., M. A. Radwan, and Mohammed M. Shabat. "Highly nonlinear Ising model and social segregation." arXiv preprint arXiv:1106.5574 (2011).
  • Rahimian, Mohammad Amin, and Ali Jadbabaie. "Naive social learning in Ising networks." American Control Conference (ACC), 2016. American Automatic Control Council (AACC), 2016.
  • Ishii, Mitsuru. "Analysis of the growth of social networking services based on the ising type agent model." Analysis(2016).
  • Oh, Wonseok, and Sangyong Jeon. "Membership herding and network stability in the open source community: The Ising perspective." Management science 53.7 (2007): 1086-1101.
  • Giannoccaro, Ilaria, Ilario De Vincenzo, and Giuseppe Carbone. "An Ising-based approach to the study of inter-organizational team dynamics." 2014 IEEE International Conference on Industrial Engineering and Engineering Management. IEEE, 2014.
  • Chen, Shu-Heng, Chia-Ling Chang, and Yi-Heng Tseng. "Social networks, social interaction and macroeconomic dynamics: How much could Ernst Ising help DSGE?." Research in International Business and Finance 30 (2014): 312-335.

2-Economy and Finance

  • Xin, C., G. Yang, and J. P. Huang. "Ising game: Nonequilibrium steady states of resource-allocation systems." Physica A: Statistical Mechanics and its Applications (2016).
  • Ko, Bonggyun, Jae Wook Song, and Woojin Chang. "Simulation of financial market via nonlinear Ising model." International Journal of Modern Physics C 27.04 (2016): 1650038.
  • Fang, Wen, et al. "Linking market interaction intensity of 3D Ising type financial model with market volatility." Physica A: Statistical Mechanics and its Applications (2016).
  • Horvath, Philip A., Kelly R. Roos, and Amit Sinha. "An Ising spin state explanation for financial asset allocation." Physica A: Statistical Mechanics and its Applications 445 (2016): 112-116.
  • Eckrot, A., J. Jurczyk, and I. Morgenstern. "Ising model of financial markets with many assets." Physica A: Statistical Mechanics and its Applications 462 (2016): 250-254.
  • Zhang, Bo, Jun Wang, and Wen Fang. "Volatility behavior of visibility graph EMD financial time series from Ising interacting system." Physica A: Statistical Mechanics and its Applications 432 (2015): 301-314.
  • Slanina, František. "Minority Game: An “Ising Model” of Econophysics." Order, Disorder and Criticality: Advanced Problems of Phase Transition TheoryVolume 3 (2012): 201.
  • Vangheli, Dorina Andru, and Gheorghe Ardelean. "The ising like statistical models for studying the dynamics of the financial stock markets." arXiv preprint cond-mat/0010318 (2000).
  • Bornholdt, Stefan, and Friedrich Wagner. "Stability of money: phase transitions in an Ising economy." Physica A: Statistical Mechanics and its Applications 316.1 (2002): 453-468.
  • Sornette, Didier. "Physics and financial economics (1776–2014): puzzles, Ising and agent-based models." Reports on Progress in Physics 77.6 (2014): 062001.
  • Sornette, Didier, and Wei-Xing Zhou. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets." Physica A: Statistical Mechanics and its Applications 370.2 (2006): 704-726.
  • Fang, Wen, and Jun Wang. "Fluctuation behaviors of financial time series by a stochastic Ising system on a Sierpinski carpet lattice." Physica A: Statistical Mechanics and Its Applications 392.18 (2013): 4055-4063.
  • Zhou, W-X., and Didier Sornette. "Self-organizing Ising model of financial markets." The European Physical Journal B 55.2 (2007): 175-181.


  • Weber, Marc, and Javier Buceta. "The cellular Ising model: a framework for phase transitions in multicellular environments." Journal of The Royal Society Interface 13.119 (2016): 20151092.
  • Vtyurina, Natalia N., et al. "Hysteresis in DNA compaction by Dps is described by an Ising model." Proceedings of the National Academy of Sciences (2016): 201521241.
  • Anna Maltsev, Victor Maltsev, Michael Stern. Clusters of calcium release channels harness the Ising phase transition to confine their elementary intracellular signals.
  • Noble, Andrew E., Jonathan Machta, and Alan Hastings. "Emergent long-range synchronization of oscillating ecological populations without external forcing described by Ising universality." Nature communications 6 (2015).
  • Li, Xumeng, et al. "Identifying differentially expressed genes in cancer patients using a non‐parameter Ising model." Proteomics 11.19 (2011): 3845-3852.
  • Lobanov, Michail Yu, and Oxana V. Galzitskaya. "The Ising model for prediction of disordered residues from protein sequence alone." Physical biology 8.3 (2011): 035004.
  • Muñoz, Victor. "What can we learn about protein folding from Ising-like models?." Current opinion in structural biology 11.2 (2001): 212-216.
  • Liu, Yi, and James P. Dilger. "Application of the one-and two-dimensional Ising models to studies of cooperativity between ion channels." Biophysical journal 64.1 (1993): 26.
  • Rice, John Jeremy, et al. "Ising model of cardiac thin filament activation with nearest-neighbor cooperative interactions." Biophysical journal 84.2 (2003): 897-909.
  • Majewski, Jacek, Hao Li, and Jurg Ott. "The Ising model in physics and statistical genetics." The American Journal of Human Genetics 69.4 (2001): 853-862.
  • Baran, Robert H., and Hanseok Ko. "An Ising model of transcription polarity in bacterial chromosomes." Physica A: Statistical Mechanics and its Applications 362.2 (2006): 403-422.
  • Schlicht, Robert, and Yoh Iwasa. "Forest gap dynamics and the Ising model." Journal of theoretical biology 230.1 (2004): 65-75.
  • Kizaki, Shinya, and Makoto Katori. "Analysis of canopy-gap structures of forests by Ising-Gibbs states-equilibrium and scaling property of real forests." Journal of the Physical Society of Japan 68.8 (1999): 2553-2560.
  • Katori, Makoto, et al. "Forest dynamics with canopy gap expansion and stochastic Ising model." Fractals 6.01 (1998): 81-86.


  • Abeyasinghe, Pubuditha M. Structure-Function Relationship of the Brain: A comparison between the 2D Classical Ising model and the Generalized Ising model. Diss. The University of Western Ontario, 2015.
  • Stramaglia, Sebastiano, et al. "Conserved Ising Model on the Human Connectome." arXiv preprint arXiv:1509.02697 (2015).
  • Das, T. K., et al. "Highlighting the structure-function relationship of the brain with the ising model and graph theory." BioMed research international 2014 (2014).
  • Marinazzo, Daniele, et al. "Information transfer and criticality in the ising model on the human connectome." PloS one 9.4 (2014): e93616.
  • Barton, John, and Simona Cocco. "Ising models for neural activity inferred via selective cluster expansion: structural and coding properties." Journal of Statistical Mechanics: Theory and Experiment 2013.03 (2013): P03002.
  • Haslinger, Robert, et al. "Missing mass approximations for the partition function of stimulus driven Ising models." Frontiers in computational neuroscience 7 (2013).
  • Schaub, Michael T., and Simon R. Schultz. "The Ising decoder: reading out the activity of large neural ensembles." Journal of computational neuroscience 32.1 (2012): 101-118.
  • Hertz, John A., et al. "Inferring network connectivity using kinetic Ising models." BMC Neuroscience 11.1 (2010): 1.
  • Tkacik, Gasper, et al. "Spin glass models for a network of real neurons." arXiv preprint arXiv:0912.5409 (2009).
  • Tkacik, Gasper, et al. "Ising models for networks of real neurons." arXiv preprint q-bio/0611072 (2006).

5-Complex Systems & General Things:

  • Collet, Francesca, Marco Formentin, and Daniele Tovazzi. "Rhythmic behavior in a two-population mean-field Ising model." Physical Review E 94.4 (2016): 042139.
  • Ren, Yihui, Stephen Eubank, and Madhurima Nath. "From network reliability to the Ising model: A parallel scheme for estimating the joint density of states." Physical Review E 94.4 (2016): 042125.
  • Morales, Irving O., et al. "Behavior of early warnings near the critical temperature in the two-dimensional Ising model." PloS one 10.6 (2015): e0130751.
  • del Campo, Abraham Martin, Sarah Cepeda, and Caroline Uhler. "Exact goodness-of-fit testing for the Ising model." arXiv preprint arXiv:1410.1242 (2014).
  • Mora, Fernando, et al. "Around the Ising Model." Nonlinear Dynamics: Materials, Theory and Experiments. Springer International Publishing, 2016. 329-345.
  • Suzuki, Hideyuki, Jun-ichi Imura, and Kazuyuki Aihara. "Chaotic Ising-like dynamics in traffic signals." Scientific reports 3 (2013): 1127.
  • Hooyberghs, Hans, et al. "Ising model for distribution networks." Philosophical Magazine 92.1-3 (2012): 168-191.
  • Băutu, Andrei, and Henri Luchian. "Particle Swarm Optimization with spanning tree representation for Ising spin glasses." IEEE Congress on Evolutionary Computation. IEEE, 2010.
  • Nisoli, Cristiano. "Nano-Ising." New Journal of Physics 18.2 (2016): 021007.


  • Wu, X-T., D. B. Abraham, and Joseph O. Indekeu. "Apparent first-order wetting and anomalous scaling in the two-dimensional Ising model." Physical review letters 116.4 (2016): 046101.
  • Binder, K., and D. P. Landau. "Wetting and layering in the nearest-neighbor simple-cubic Ising lattice: A Monte Carlo investigation." Physical Review B 37.4 (1988): 1745.
  • Lukas, D., E. Glazyrina, and N. Pan. "Computer simulation of liquid wetting dynamics in fiber structures using the Ising model." Journal of the Textile Institute 88.2 (1997): 149-161.

7-Casimir effects

  • Machta, Benjamin B., Sarah L. Veatch, and James P. Sethna. "Critical Casimir forces in cellular membranes." Physical review letters 109.13 (2012): 138101.
  • Fukuto, Masafumi, Yohko F. Yano, and Peter S. Pershan. "Critical Casimir effect in three-dimensional Ising systems: measurements on binary wetting films." Physical review letters 94.13 (2005): 135702.
  • Abraham, Douglas B., and Anna Maciołek. "Surface states and the Casimir interaction in the Ising model." EPL (Europhysics Letters) 101.2 (2013): 20006.


  • Mariani, M. C., et al. "Ising type models applied to Geophysics and high frequency market data." Physica A: Statistical Mechanics and its Applications 390.23 (2011): 4396-4402.

9-Models inspired by the Ising model

  • Sznajd social model: Sznajd-Weron, Katarzyna, and Jozef Sznajd. "Opinion evolution in closed community." International Journal of Modern Physics C 11.06 (2000): 1157-1165.
  • Hopfield neural model: Hopfield, John J. "Neural networks and physical systems with emergent collective computational abilities." Proceedings of the national academy of sciences 79.8 (1982): 2554-2558.
  • Majority-vote model: de Oliveira, Mário J. "Isotropic majority-vote model on a square lattice." Journal of Statistical Physics 66.1-2 (1992): 273-281.
  • Glauber Model: Glauber, Roy J. "Time‐dependent statistics of the Ising model." Journal of mathematical physics 4.2 (1963): 294-307.

10-History of the model:

  • Brush, Stephen G. "History of the Lenz-Ising model." Reviews of modern physics 39.4 (1967): 883.
  • Niss, Martin. "History of the Lenz-Ising model 1920–1950: from ferromagnetic to cooperative phenomena." Archive for history of exact sciences 59.3 (2005): 267-318.
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