Temporary HW: Difference between revisions
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==Problem 1: == | ==Problem 1: Three Ising spins == | ||
Assume three spins <math> s_1, s_2, s_3 </math> are arranged in an equilateral triangle with each spin interacting with its two neighbors. The energy expression for the Ising model in an external magnetic field <math> H </math> is give by: | |||
= | <math> H=-J(s_1s_2 + s_2 s_3 + s_3 s_1) - F (s_1 + s_2 + s_3) </math> | ||
==Problem 3: == | (a) Find partition function for this model. | ||
(b) Find average spin <math> \langle s \rangle </math>. | |||
(c) Find internal energy <math> E </math>. | |||
==Problem 2: Spin-spin correlation function in the Ising model == | |||
==Problem 3: Mean-field theory of the Heisenberg model of ferromagnetism == | |||
Revision as of 12:07, 7 April 2011
Problem 1: Three Ising spins
Assume three spins are arranged in an equilateral triangle with each spin interacting with its two neighbors. The energy expression for the Ising model in an external magnetic field is give by:
(a) Find partition function for this model.
(b) Find average spin .
(c) Find internal energy .
