This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: as the highest temperature for which this equation has a nonzero solution for h S i in the limit of zero applied magnetic eld. Show that this solution is the same as that found in class using the BraggWilliams approach. 3. Consider the innite range Ising model, where the coupling J ij = J for all distinct pairs of spins, with no restriction to nearest neighbors. Thus, the Hamiltonian for a system of volume V is H =B X i S iJ 2 X ij S i S j . (1) (a). Explain why this model only makes sense if J = J/N , where N is the number of spins in the system. 1 (b), Prove that exp ax 2 2 N ! = Z  dy q 2 / ( Na ) exp Na 2 y 2 + axy , (2) provided that Re a is greater than 0. (c). Hence, show that the partition function is given by Q = Z  dy q 2 k B T/ ( NJ ) eNL , (3) where L = Jy 2 21 ln [2 cosh ( ( B + Jy ))] . (4) Here = 1 / ( k B T ), where T is the absolute temperature. 2...
View
Full
Document
 Fall '05
 STROUD
 Physics

Click to edit the document details