Ising model: Difference between revisions

Revision as of 19:31, 3 January 2025

Revision as of 03:08, 11 January 2025

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<math display="block">Z(\beta) = \operatorname{Tr} \left(V^L\right) = \lambda_1^L + \lambda_2^L = \lambda_1^L \left[1 + \left(\frac{\lambda_2}{\lambda_1}\right)^L\right],</math>

where λ₁ is the highest eigenvalue of ''V'', while λ₂ is the other eigenvalue:

<math display="block">\lambda_1 = e^{\beta J} \cosh \beta h + \sqrt{e^{2\beta J} (\sinhcosh \beta h)^2 + e^{-2 \sinh 2 \beta J}},</math>

and \(|λ₂\frac{\lambda_2}{\lambda_1}| <\leq λ₁\). This gives the formula of the free energy.

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