Analytic properties of the Onsager solution of the ising model

Majumdar, Chanchal. K. (1966) Analytic properties of the Onsager solution of the ising model Physical Review, 145 (1). pp. 158-163. ISSN 0031-899X

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The analytic properties of the Onsager solution of the two-dimensional Ising lattice in zero external magnetic field are investigated. The free energy above the critical temperature Tc can be regarded as an analytic function in the u plane, where u=exp(-4J/kBT), with singularities at u=0, ∞, and exp(±4J/kBTc). But its analytic continuation below the critical temperature does not describe a stable thermodynamic phase. Similar statements are true for the free energy below the critical temperature. The famous logarithmic singularity is briefly discussed. Finally, the knowledge of the analytic properties is shown, by elementary considerations, to explain the nonanalytic behavior at vanishing external field below the critical temperature-a result first enunciated by Yang and Lee for the free energy in the presence of an external magnetic field.

Item Type:Article
Source:Copyright if this article belongs to The American Physical Society.
ID Code:33174
Deposited On:30 Mar 2011 10:55
Last Modified:30 Mar 2011 10:55

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