445lec32 - PHYS 445 Lecture 32 - Ising model Lecture 32 -...

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PHYS 445 Lecture 32 - Ising model 32 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 32 - Ising model What's Important: Ising model in 3D Text : Reif Ising model In the previous lecture, we considered the effects of dimensionality on the existence of phase transitions, using a spin system as an example. Let's now examine the properties of this system, which is called the Ising model, in three dimensions. Comments: The Ising model in two dimensions has been solved exactly by Onsager, although the proof is difficult. Reif also considers systems subject to magnetic fields, and extends the results here for spin - 1/2 to systems with general spin S . One form often used to represent the interaction energy between two objects with spin vectors S j and S k is the so-called Heisenberg model [ energy ] -2 J S j S k (Heisenberg) (32.1) where J > 0 makes the interaction attractive the factor of 2 is chosen to ease the normalization later. This form also appears for systems where the energy is proportional to the sum of spin
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This note was uploaded on 09/07/2009 for the course PHYS 445 taught by Professor Davidboal during the Spring '08 term at Simon Fraser.

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445lec32 - PHYS 445 Lecture 32 - Ising model Lecture 32 -...

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