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 equa-tion 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 Bragg-Williams 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 i-J 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 ) e-NL , (3) where L = Jy 2 2-1 ln [2 cosh ( ( B + Jy ))] . (4) Here = 1 / ( k B T ), where T is the absolute temperature. 2...
View Full Document
- Fall '05