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04 07 retrieved 2013 04 21 peierls r 1936 on ising s model of ferromagnetism mathematical proceedings of the cambridge philosophical society 32 3 477 481 bibcode 1936pcps 32 477p doi 10 1017 s0305004100019174 s2cid 122630492 1 2 3 montroll potts ward 1963 pp 308 309 simon barry 1980 10 01 correlation inequalities and the decay of correlations in ferromagnets communications in mathematical physics 77 2 111 126 bibcode 1980cmaph 77 111s doi 10 1007 bf01982711 issn 1432 0916 s2cid 17543488 duminil copin hugo tassion vincent 2016 04 01 a new proof of the sharpness of the phase transition for bernoulli percolation and the ising model communications in mathematical physics 343 2 725 745 arxiv 1502 03050 bibcode 2016cmaph 343 725d doi 10 1007 s00220 015 2480 z issn 1432 0916 s2cid 119330137 beffara vincent duminil copin hugo 2012 08 01 the self dual point of the two dimensional random cluster model is critical for q 1 probability theory and related fields 153 3 511 542 doi 10 1007 s00440 011 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mehmet 2014 effective ergodicity in single spin flip dynamics physical review e 90 3 032141 arxiv 1405 4497 bibcode 2014phrve 90c2141s doi 10 1103 physreve 90 032141 pmid 25314429 external links edit wikimedia commons has media related to ising model ising model at the net advance of physics barry arthur cipra the ising model is np complete siam news vol 33 no 6 online edition pdf science world article on the ising model a dynamical 2d ising java applet by ucsc archived 2020 02 21 at the wayback machine a dynamical 2d ising java applet a larger more complicated 2d ising java applet archived 2020 11 25 at the wayback machine i sing well tempered the ising model a simple model for critical behavior in a system of spins by dirk brockman is an interactive simulation that allows users to export the working code to a presentation slide ising model simulation by enrique zeleny the wolfram demonstrations project phase transitions on lattices three dimensional proof for ising model impossible sandia researcher claims interactive monte carlo simulation of the ising xy and heisenberg models with 3d graphics requires webgl compatible browser ising model code image denoising example with ising model david tong s lecture notes provide a good introduction the cartoon picture of magnets that has transformed science quanta magazine article about ising model simulation of the 2 dimensional ising model in julia https github com cossio squareisingmodel jl v t e stochastic processes discrete time bernoulli process branching process chinese restaurant process galton watson process independent and identically distributed random variables markov chain moran process random walk loop erased self avoiding biased maximal entropy continuous time additive process airy process bessel process birth death process pure birth brownian motion bridge dyson excursion fractional geometric meander cauchy process contact process continuous time random walk cox process diffusion process empirical process 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