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TheMathCat (talk | contribs) Born is not an author of that article but the editor who handled it |
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<math display="block">\langle \sigma_i \sigma_j \rangle_\beta \geq c(\beta) > 0.</math>
This was first proven by [[Rudolf Peierls]] in 1936,<ref>{{Cite journal |doi=10.1017/S0305004100019174 |title=On Ising's model of ferromagnetism |journal=[[Mathematical Proceedings of the Cambridge Philosophical Society]] |volume=32 |issue=3 |pages=477 |year=1936 |last1=Peierls |first1=R
The Ising model on a two-dimensional square lattice with no magnetic field was analytically solved by {{harvs|txt|authorlink=Lars Onsager|first=Lars |last=Onsager|year=1944}}. Onsager obtained the [[correlation function]]s and [[Thermodynamic free energy|free energy]] of the Ising model and announced the formula for the [[spontaneous magnetization]] for the 2-dimensional model in 1949 but did not give a derivation. {{harvtxt|Yang|1952}} gave the first published proof of this formula, using a [[Szegő limit theorems|limit formula]] for [[Fredholm determinant]]s, proved in 1951 by [[Gábor Szegő|Szegő]] in direct response to Onsager's work.<ref name="Montroll 1963 pages=308-309">{{harvnb|Montroll|Potts|Ward|1963|pages=308–309}}</ref>
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