p212mid06sols - Physics 212: Statistical mechanics II, Fall...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Physics 212: Statistical mechanics II, Fall 2006 Midterm solutions : test given Thursday, 11/15/06 1. (a) To get the ritical exponent , we need to compute the response to a magnetic field when T- T c . The Landau free energy in a small magnetic field is F ( m ) = ahm + bm 6 (1) where the quartic term is absent because we are describing a tricritical point. Minimizing gives m 5 h , or = 5. (b) A good set of sketches should show the following information. For T > T c , the response is linear near h = 0. For T = T c , the response shows the power-law related to for small h . For T < T c , there is a jump in the magnetization at H = 0, and this jump is of magnitude going as ( T c- T ) . 2. (a) The value of h S x i in the appropriate density matrix is zero. (b) The value of h S z i is h 2 tanh( h z /k B T ) . (c) If the perturbation commutes with the original Hamiltonian, as in this case, then it induces no transitions, and expectation values are unchanged....
View Full Document

This note was uploaded on 08/01/2008 for the course PHYSICS 212 taught by Professor Moore during the Fall '06 term at University of California, Berkeley.

Page1 / 2

p212mid06sols - Physics 212: Statistical mechanics II, Fall...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online