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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 λ<sub>1</sub> is the highest eigenvalue of ''V'', while {{mvar|λ<sub>2</sub>}} 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}=e^{\beta J} \cosh \beta h + \sqrt{e^{2\beta J} (\sinh \beta h)^2
and {{mvar|λ<sub>2</sub> < λ<sub>1</sub>}}. 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>
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