PHZ3400 Midterm Two Solution: Difference between revisions

@@ Line 1: / Line 1: @@
-==PHZ 3400 – Midterm Two Exam (with solutions) – April 10, 2009==
-===Problem 1===
-'' Explain the concept of the "Thermodynamic Limit", and present the corresponding domain wall argument (derivation of a formula) to estimate the relaxation time as a function of system size, at T < Tc.''
-The partition function which applies in this case is
-<math>Z = \sum_{n}^{\infty}\varepsilon^{-\beta E_n}</math>  where n = the number of particles.
-When systems are sufficiently large, <math> n\rightarrow \infty</math>, they reach the thermodynamic limit and symmetry breaking can occur.  However, symmetry breaking, including phase transitions, cannot occur for any finite system.[1]
-[1]  [http://prola.aps.org/abstract/PR/v87/i3/p404_1
-C. N. Yang and T. D. Lee, ''Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation'' Phys. Rev. 87, 404 - 409 (1952)]
-===Problem 2===
-''Sketch the magnetization of a ferromagnet as a function of temperature T, for (A) Zero external magnetic field and (B) Finite external magnetic field.  How is the behavior around the Curie Temperature (Tc) affected by the field?''
-===Problem 3===
-===Problem 4===

Latest revision as of 20:43, 17 March 2011