PHZ3400 Midterm Two Solution: Difference between revisions
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'' 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.'' | '' 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=number of particles. | 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=== | ===Problem 2=== | ||
Revision as of 16:11, 15 April 2009
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 where n = the number of particles. When systems are sufficiently large, , 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?