Ising model: Difference between revisions

Revision as of 03:08, 11 January 2025

Revision as of 03:18, 11 January 2025

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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} (\cosh \beta h)^2 -2 \sinh 2 \beta J},</math>

and \($|\frac{\lambda_2}{\lambda_1}| \leq 1\)$. This gives the formula of the free energy above. In the thermodynamics limit for the non-interaction case (J = 0), we got

<math display="block">Z_N \to (\lambda_1)^N = (2\cosh \beta h)^N,</math>

as the answer for the open-boundary Ising model.

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