419
Views
103
CrossRef citations to date
0
Altmetric
Original Articles

An Introduction to the Ising Model

Pages 937-959 | Published online: 18 Apr 2018

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (7)

Miriam K. Forbes, Aidan G. C. Wright, Kristian E. Markon & Robert F. Krueger. (2021) Quantifying the Reliability and Replicability of Psychopathology Network Characteristics. Multivariate Behavioral Research 56:2, pages 224-242.
Read now
Matthew Richey. (2010) The Evolution of Markov Chain Monte Carlo Methods. The American Mathematical Monthly 117:5, pages 383-413.
Read now
Jonathan David Farley. (2007) Evolutionary Dynamics of the Insurgency in Iraq: A Mathematical Model of the Battle for Hearts and Minds. Studies in Conflict & Terrorism 30:11, pages 947-962.
Read now
N. Pan & W. Zhong. (2006) Fluid Transport Phenomena in Fibrous Materials. Textile Progress 38:2, pages 1-93.
Read now
Russell Merris. (1995) A survey of graph laplacians. Linear and Multilinear Algebra 39:1-2, pages 19-31.
Read now
Peter D. Lax. (1989) Writing Mathematics Well. By Leonard Gillman. The American Mathematical Monthly 96:4, pages 380-381.
Read now
James P. Coughlin & Robert H. Baran. (1988) Letters to the Editor. The American Mathematical Monthly 95:7, pages 631-633.
Read now

Articles from other publishers (96)

Jianwen MaQinyou HuTian LiuZhaoxin ZhuYue Zhou. (2024) Research on Ship Collision Risk Calculation in Port Navigation Waters Based on Ising Model and AIS Data. ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering 10:2.
Crossref
Bing Liu, Yifang Ma, Jin Zhang, Yi Kuang, Junjie Bian & Xin Jiang. (2024) Unveiling urban traffic accessibility patterns and phase diagrams of traffic direction through real-time navigation data in Beijing. Information Processing & Management 61:3, pages 103660.
Crossref
Zhiqiang Liao, Kaijie Ma, Md Shamim Sarker, Hiroyasu Yamahara, Munetoshi Seki & Hitoshi Tabata. (2024) Overdamped Ising machine with stochastic resonance phenomena in large noise condition. Nonlinear Dynamics.
Crossref
Junggu Choi, Kion Kim, Soo Hyun Park, Juyoen Hur, Hyunjung Yang, Young-Hoon Kim, Hakbae Lee & Sanghoon Han. (2024) Investigation of factors regarding the effects of COVID-19 pandemic on college students’ depression by quantum annealer. Scientific Reports 14:1.
Crossref
Jaehyun Kim, Joon‐Kyu Han, Ho‐Young Maeng, Janguk Han, Jeong Woo Jeon, Yoon Ho Jang, Kyung Seok Woo, Yang‐Kyu Choi & Cheol Seong Hwang. (2024) Fully CMOS‐Based p‐Bits with a Bistable Resistor for Probabilistic Computing. Advanced Functional Materials.
Crossref
Marvin Lücke, Stefanie Winkelmann, Jobst Heitzig, Nora Molkenthin & Péter Koltai. (2024) Learning interpretable collective variables for spreading processes on networks. Physical Review E 109:2.
Crossref
Guilherme Bonifácio Rosa, Luis Henrique da Silveira Lacerda & Sergio Ricardo de Lazaro. (2024) Influence of the oxygen vacancy and Ag-doping on the magnetic and electronic properties of the SrFeO3 material. Journal of Magnetism and Magnetic Materials 591, pages 171715.
Crossref
Siying Zhu, Elijah Borodin & Andrey P. Jivkov. (2024) Discrete modelling of continuous dynamic recrystallisation by modified Metropolis algorithm. Computational Materials Science 234, pages 112804.
Crossref
P. Åhag, R. Czyż & P.H. Lundow. (2024) On a generalised Lambert W branch transition function arising from p,q-binomial coefficients. Applied Mathematics and Computation 462, pages 128347.
Crossref
Zekeriya Ender Eğer & Pınar Acar. (2024) Uncertainty quantification of phase transitions in magnetic materials lattices. Applied Physics Letters 124:2.
Crossref
Imon Mukherjee & Goutam Paul. (2023) High capacity secure dynamic multi-bit data hiding using Fibonacci Energetic pixels. Multimedia Tools and Applications 83:2, pages 5181-5206.
Crossref
Gabor KorvinGabor Korvin. 2024. Statistical Rock Physics. Statistical Rock Physics 339 379 .
S. Ait Jmal, M. Ait Tamerd, O. Mounkachi, J.P. Salvestrini & M. Balli. (2023) Investigation of the electronic, magnetic, exchange interactions, and magnetocaloric properties in orthotitanate oxides RTiO3 (R = Er, Ho). Materials Today Communications 37, pages 107324.
Crossref
Sigeng Chen, Jeffrey S. Rosenthal, Aki Dote, Hirotaka Tamura & Ali Sheikholeslami. (2023) Optimization via Rejection-Free Partial Neighbor Search. Statistics and Computing 33:6.
Crossref
Joonsoo Kim, Yuki Kimura, Brian Puchala, Tomoya Yamazaki, Udo Becker & Wenhao Sun. (2023) Dissolution enables dolomite crystal growth near ambient conditions. Science 382:6673, pages 915-920.
Crossref
Carlos Navarrete, Mariana Macedo, Rachael Colley, Jingling Zhang, Nicole Ferrada, Maria Eduarda Mello, Rodrigo Lira, Carmelo Bastos-Filho, Umberto Grandi, Jérôme Lang & César A. Hidalgo. (2023) Understanding political divisiveness using online participation data from the 2022 French and Brazilian presidential elections. Nature Human Behaviour 8:1, pages 137-148.
Crossref
María del Sol Reyes-Ortiz, Josué Manik Nava-Sedeño & Andreas Deutsch. (2023) The dichotomous role of anisotropic sensing in pattern generation and disruption. Physica A: Statistical Mechanics and its Applications 630, pages 129261.
Crossref
Tomasz F. Stepinski & Jakub Nowosad. (2023) The kinetic Ising model encapsulates essential dynamics of land pattern change. Royal Society Open Science 10:10.
Crossref
Hyundo Jung, Hyunjin Kim, Woojin Lee, Jinwoo Jeon, Yohan Choi, Taehyeong Park & Chulwoo Kim. (2023) A quantum-inspired probabilistic prime factorization based on virtually connected Boltzmann machine and probabilistic annealing. Scientific Reports 13:1.
Crossref
BingJin Chen, Yubo Hou, Chee Kwan Gan & Minggang Zeng. (2023) Micromagnetic realization of energy-based models using stochastic magnetic tunnel junctions. Applied Physics A 129:9.
Crossref
Geonhyeong Park, Yun‐Seok Choi, S. Joon Kwon & Dong Ki Yoon. (2023) Planar Spin Glass with Topologically Protected Mazes in the Liquid Crystal Targeting for Reconfigurable Micro Security Media. Advanced Materials 35:36.
Crossref
Hao Lo, William Moy, Hanzhao Yu, Sachin Sapatnekar & Chris H. Kim. (2023) An Ising solver chip based on coupled ring oscillators with a 48-node all-to-all connected array architecture. Nature Electronics 6:10, pages 771-778.
Crossref
Hamidreza Oliaei-Moghadam, Chané Moodley & Mahmood Hosseini-Farzad. (2023) Patterns for all-digital quantum ghost imaging generated by the Ising model. Optics & Laser Technology 163, pages 109392.
Crossref
Alejandro Gallegos & Jianzhong Wu. (2023) Hierarchical Model of Weak Polyelectrolytes with Ionization and Conformation Consistency. Macromolecules 56:12, pages 4760-4772.
Crossref
Tomasz F Stepinski. (2023) Spatially explicit simulation of deforestation using the Ising-like neutral model. Environmental Research: Ecology 2:2, pages 025003.
Crossref
Junyi Gao, Joerg Heintz, Christina Mack, Lucas Glass, Adam Cross & Jimeng Sun. (2023) Evidence-driven spatiotemporal COVID-19 hospitalization prediction with Ising dynamics. Nature Communications 14:1.
Crossref
Qiankun Wang, Xingchen Li, Bingzhe Wu, Ke Yang, Wei Hu, Guangyu Sun & Yuchao Yang. (2023) COPPER: a combinatorial optimization problem solver with processing-in-memory architectureCOPPER: 具有存内计算架构的组合优化问题求解器. Frontiers of Information Technology & Electronic Engineering 24:5, pages 731-741.
Crossref
Hyunsuk Hong, Kevin P. O'Keeffe, Jae Sung Lee & Hyunggyu Park. (2023) Swarmalators with thermal noise. Physical Review Research 5:2.
Crossref
Qian Du, Kui Cao & Su-Peng Kou. (2023) Non-Hermitian Ising model at finite temperature. Communications in Theoretical Physics 75:4, pages 045701.
Crossref
Baofang Cai, Yihan He, Yue Xin, Zhengping Yuan, Xue Zhang, Zhifeng Zhu & Gengchiau Liang. (2023) Unconventional computing based on magnetic tunnel junction. Applied Physics A 129:4.
Crossref
Minghao Liu, Lei Zhang, Junxian Liu, Tsz Lok Wan, Aijun Du, Yuantong Gu & Liangzhi Kou. (2023) Density Functional Theory Studies on Magnetic Manipulation in NiI 2 Layers . ACS Applied Electronic Materials 5:2, pages 920-927.
Crossref
Megan C. Giron, Georgios Korpas, Waqas Parvaiz, Prashant Malik & Johannes Aspman. (2023) Approaching Collateral Optimization for NISQ and Quantum-Inspired Computing (May 2023). IEEE Transactions on Quantum Engineering 4, pages 1-18.
Crossref
S. Ait Jmal, M. Balli, H. Bouhani & O. Mounkachi. (2023) On the electronic and magnetic properties of RVO3 (R = Er, Ho, Y, Lu) vanadates: first principles study. Materials Chemistry and Physics 294, pages 127058.
Crossref
Thomas Schmickl. (2022) Strong Emergence Arising from Weak Emergence. Complexity 2022, pages 1-17.
Crossref
Jing Gu & Kai Zhang. (2022) Thermodynamics of the Ising Model Encoded in Restricted Boltzmann Machines. Entropy 24:12, pages 1701.
Crossref
Tomasz F. Stepinski. (2022) Curb your enthusiasm for explaining the complexity of landscape configurations in terms of thermodynamics. Landscape Ecology 37:11, pages 2735-2741.
Crossref
Xi Jiang, Guanghua Xiao & Qiwei Li. (2022) A Bayesian modified Ising model for identifying spatially variable genes from spatial transcriptomics data. Statistics in Medicine 41:23, pages 4647-4665.
Crossref
Karola Kaefer, Federico Stella, Bruce L. McNaughton & Francesco P. Battaglia. (2022) Replay, the default mode network and the cascaded memory systems model. Nature Reviews Neuroscience 23:10, pages 628-640.
Crossref
Kyung Seok Woo, Jaehyun Kim, Janguk Han, Woohyun Kim, Yoon Ho Jang & Cheol Seong Hwang. (2022) Probabilistic computing using Cu0.1Te0.9/HfO2/Pt diffusive memristors. Nature Communications 13:1.
Crossref
Einar Gabbassov. (2022) Transit facility allocation: Hybrid quantum-classical optimization. PLOS ONE 17:9, pages e0274632.
Crossref
A. O. Korol, K. V. Nevedev & V. Yu. Kapitan. (2022) Neural Network Method for Calculation of the Curie Point of the Two-Dimensional Ising Model. SIBERIAN JOURNAL OF PHYSICS 17:2, pages 5-15.
Crossref
Alexandre L.M. Levada. (2022) On the numerical computation of Fisher–Rao based distances and KL-divergences between Gaussian random fields. Journal of Computational Science 62, pages 101714.
Crossref
Gilead Posluns, Yan Zhu, Guowei Zhang & Mark C. Jeffrey. (2022) A scalable architecture for reprioritizing ordered parallelism. A scalable architecture for reprioritizing ordered parallelism.
Arash Komaee. (2022) On the Dynamics of Interacting Agents on an Ising Lattice. On the Dynamics of Interacting Agents on an Ising Lattice.
Yang Tian & Pei Sun. (2022) Information thermodynamics of encoding and encoders. Chaos: An Interdisciplinary Journal of Nonlinear Science 32:6.
Crossref
Huan Wang, Chuang Ma, Han-Shuang Chen, Ying-Cheng Lai & Hai-Feng Zhang. (2022) Full reconstruction of simplicial complexes from binary contagion and Ising data. Nature Communications 13:1.
Crossref
Patrick Huembeli, Juan Miguel Arrazola, Nathan Killoran, Masoud Mohseni & Peter Wittek. (2022) The physics of energy-based models. Quantum Machine Intelligence 4:1.
Crossref
Arkaprava Roy & Subhashis Ghosal. (2022) Optimal Bayesian smoothing of functional observations over a large graph. Journal of Multivariate Analysis 189, pages 104876.
Crossref
Andrew D.P. Smith, Peter T. Haugen & Boyd F. Edwards. (2022) Hysteretic transition between states of a filled hexagonal magnetic dipole cluster. Journal of Magnetism and Magnetic Materials 549, pages 168991.
Crossref
Paweł Sowa & Daria Zychma. (2022) Dynamic Equivalents in Power System Studies: A Review. Energies 15:4, pages 1396.
Crossref
Saul Gonzalez-Bermejo, Guillermo Alonso-Linaje & Parfait Atchade-Adelomou. (2022) GPS: A New TSP Formulation for Its Generalizations Type QUBO. Mathematics 10:3, pages 416.
Crossref
Andrzej Paszkiewicz, Bartosz Pawłowicz, Bartosz Trybus & Mateusz Salach. (2021) Traffic Intersection Lane Control Using Radio Frequency Identification and 5G Communication. Energies 14:23, pages 8066.
Crossref
Peng Lu, Zhuo Zhang & Mengdi Li. (2021) Big data-drive agent-based modeling of online polarized opinions. Complex & Intelligent Systems 7:6, pages 3259-3276.
Crossref
Yelena Y Bernadskaya, Haicen Yue, Calina Copos, Lionel Christiaen & Alex Mogilner. (2021) Supracellular organization confers directionality and mechanical potency to migrating pairs of cardiopharyngeal progenitor cells. eLife 10.
Crossref
Yunyi Shen, Erik R. Olson & Timothy R. Van Deelen. (2021) Spatially explicit modeling of community occupancy using Markov Random Field models with imperfect observation: Mesocarnivores in Apostle Islands National Lakeshore. Ecological Modelling 459, pages 109712.
Crossref
Gargi Agrahari & Abhijit Chatterjee. (2021) Thermodynamic calculations using reverse Monte Carlo. Physical Review E 104:4.
Crossref
Xiaowen Dong, Dorina Thanou, Michael Rabbat & Pascal Frossard. 2021. Graph Spectral Image Processing. Graph Spectral Image Processing 31 61 .
Hyeong In Choi, Sungjin Lee, Hwan Pyo Moon, Nam-Sook Wee, Daehoon Kim & Song-Hwa Kwon. (2021) Seeded Ising Model and Distributed Biometric Template Storage and Matching. Entropy 23:7, pages 849.
Crossref
Yue Wang, Boyu Zhang, Jérémie Kropp & Nadya Morozova. (2021) Inference on tissue transplantation experiments. Journal of Theoretical Biology 520, pages 110645.
Crossref
Joseph Geraci. (2021) Shattering cancer with quantum machine learning: A preview. Patterns 2:6, pages 100281.
Crossref
Gianluca Caposciutti, Mirko Marracci, Carlo Trigona, Salvatore Baglio & Bernardo Tellini. (2021) Investigation of a 100 µm Magnetic Wire for Temperature Sensing based on a Time Domain Readout. Investigation of a 100 µm Magnetic Wire for Temperature Sensing based on a Time Domain Readout.
Enrique Hernández-Lemus. (2021) Random Fields in Physics, Biology and Data Science. Frontiers in Physics 9.
Crossref
Pubuditha M. Abeyasinghe, Marco Aiello, Carlo Cavaliere, Adrian M. Owen & Andrea Soddu. (2021) A comparison of diffusion tractography techniques in simulating the generalized Ising model to predict the intrinsic activity of the brain. Brain Structure and Function 226:3, pages 817-832.
Crossref
Edwin Bedolla, Luis Carlos Padierna & Ramón Castañeda-Priego. (2020) Machine learning for condensed matter physics. Journal of Physics: Condensed Matter 33:5, pages 053001.
Crossref
Douglas Lind & Brian Marcus. 2020. An Introduction to Symbolic Dynamics and Coding. An Introduction to Symbolic Dynamics and Coding.
Andrzej Paszkiewicz & Jan Węgrzyn. (2020) Responsiveness of the Sensor Network to Alarm Events Based on the Potts Model. Sensors 20:23, pages 6979.
Crossref
Charlotte Werndl & Roman Frigg. (2020) When do Gibbsian phase averages and Boltzmannian equilibrium values agree?. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 72, pages 46-69.
Crossref
Jayati Bhadra, M. Vinayaka Murthy & M. K. Banga. (2020) A novel piracy protection scheme for videos using force-induced pixels. Multimedia Tools and Applications 79:33-34, pages 25215-25236.
Crossref
Mohammad Ramshani, Xueping Li, Anahita Khojandi & Olufemi Omitaomu. (2020) An agent-based approach to study the diffusion rate and the effect of policies on joint placement of photovoltaic panels and green roof under climate change uncertainty. Applied Energy 261, pages 114402.
Crossref
Kalidas Yeturu. 2020. Principles and Methods for Data Science. Principles and Methods for Data Science 81 206 .
Lourens Waldorp, Maarten Marsman & Gunter Maris. (2018) Logistic regression and Ising networks: prediction and estimation when violating lasso assumptions. Behaviormetrika 46:1, pages 49-72.
Crossref
Manuel Kauers & Doron Zeilberger. (2018) A Simple Rederivation of Onsager’s Solution of the 2D Ising Model Using Experimental Mathematics. The Mathematical Intelligencer 41:1, pages 1-6.
Crossref
Francesco Regazzoni, Luca Dedè & Alfio Quarteroni. (2018) Active contraction of cardiac cells: a reduced model for sarcomere dynamics with cooperative interactions. Biomechanics and Modeling in Mechanobiology 17:6, pages 1663-1686.
Crossref
Chang Yong Han, Song-Hwa Kwon, Hyeong In Choi, Sung Jin Lee & Nam-Sook Wee. (2018) Seeded Ising model and the statistical nature of human iris templates. Physical Review E 98:3.
Crossref
Kaushik Roy, Abhronil Sengupta & Yong Shim. (2018) Perspective: Stochastic magnetic devices for cognitive computing. Journal of Applied Physics 123:21, pages 210901.
Crossref
Riet van Bork, Claudia D. van Borkulo, Lourens J. Waldorp, Angélique O. J. Cramer & Denny Borsboom. 2018. Stevens' Handbook of Experimental Psychology and Cognitive Neuroscience. Stevens' Handbook of Experimental Psychology and Cognitive Neuroscience 1 35 .
Richard F. Spaide. (2018) ISING MODEL OF CHORIOCAPILLARIS FLOW. Retina 38:1, pages 79-83.
Crossref
Charlotte Werndl & Roman Frigg. (2022) Mind the Gap: Boltzmannian versus Gibbsian Equilibrium. Philosophy of Science 84:5, pages 1289-1302.
Crossref
Andrei Bulatov, Leslie Ann Goldberg, Mark Jerrum, David Richerby & Stanislav Živný. (2017) Functional clones and expressibility of partition functions. Theoretical Computer Science 687, pages 11-39.
Crossref
Cristóbal A. Navarro, Wei Huang & Youjin Deng. (2016) Adaptive multi-GPU Exchange Monte Carlo for the 3D Random Field Ising Model. Computer Physics Communications 205, pages 48-60.
Crossref
Behtash Behin-Aein, Vinh Diep & Supriyo Datta. (2016) A building block for hardware belief networks. Scientific Reports 6:1.
Crossref
Peijie Yin & Gao-Feng Zhao. (2015) Numerical study of two-phase fluid distributions in fractured porous media. International Journal for Numerical and Analytical Methods in Geomechanics 39:11, pages 1188-1211.
Crossref
Amanda Streib, Noah Streib, Isabel Beichl & Francis Sullivan. (2015) Stratified sampling for the Ising model: A graph-theoretic approach. Computer Physics Communications 191, pages 1-8.
Crossref
Walter Vinci, Klas Markström, Sergio Boixo, Aidan Roy, Federico M. Spedalieri, Paul A. Warburton & Simone Severini. (2014) Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer. Scientific Reports 4:1.
Crossref
Xuefeng Gao, J. Tyson McDonald, Lynn Hlatky & Heiko Enderling. (2013) Acute and Fractionated Irradiation Differentially Modulate Glioma Stem Cell Division Kinetics. Cancer Research 73:5, pages 1481-1490.
Crossref
Alexander A. KokhanovskyEvgueni Kassianov, Dana E. Lane-Veron, Larry K. Berg, Mikhail Ovchinnikov & Pavlos Kollias. 2013. Light Scattering Reviews 7. Light Scattering Reviews 7 69 107 .
Yair Goldberg & Ya’acov Ritov. (2009) Local procrustes for manifold embedding: a measure of embedding quality and embedding algorithms. Machine Learning 77:1, pages 1-25.
Crossref
Jocelyn Quaintance. (2009) Word representations of proper arrays . Discrete Mathematics 309:6, pages 1199-1212.
Crossref
Timotej Jagric & Sebastjan Strasek. (2005) Efficient Market Hypothesis in the Capital Market of a Small Transition Economy - Does It Hold?. Acta Oeconomica 55:4, pages 427-452.
Crossref
Robert Kozma, Marko Puljic, Paul Balister, Bela Bollobás & Walter J. Freeman. (2005) Phase transitions in the neuropercolation model of neural populations with mixed local and non-local interactions. Biological Cybernetics 92:6, pages 367-379.
Crossref
Mark Jerrum, Jung-Bae Son, Prasad Tetali & Eric Vigoda. (2004) Elementary bounds on Poincaré and log-Sobolev constants for decomposable Markov chains. The Annals of Applied Probability 14:4.
Crossref
M. G. Eilon. (2004) Variation in field-dependence of magnetic reversal mechanism with interspin coupling and system size for a two-dimensional classical Ising lattice with barrier dynamics. Physical Review B 70:5.
Crossref
Steven R. Finch. (1999) Several constants arising in statistical mechanics. Annals of Combinatorics 3:2-4, pages 323-335.
Crossref
W. Schwärzler & D. J. A. Welsh. (2008) Knots, matroids and the Ising model. Mathematical Proceedings of the Cambridge Philosophical Society 113:1, pages 107-139.
Crossref
Mark Jerrum & Alistair Sinclair. 1990. Automata, Languages and Programming. Automata, Languages and Programming 462 475 .
Guido Fioretti. (2011) Utility, Games, and Narratives. SSRN Electronic Journal.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.