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Mean field solution for potts model

  1. Jun 25, 2015 #1
    1. The problem statement, all variables and given/known data
    The mean-field equation for the three-state Potts model H= -J∑δσiδσj can be derived as follows using this:
    a) show that H is equivalent to -J∑Si.Sj where Si=(1 0) , (-1/2 √3/2 ) , (-1/2 -√3/2)
    b) putting H0= (H0 H'0) show the mean field equation become
    H0/jz = exp(3βH0/2 ) -1 / exp(3β H0/2) +2
    Fmf= - N kT Ln( exp(β H0) +2 exp (-β H0/2) + N H0^2 / 2 Jz

    it is problem 4.3 statistical mechanics of phase transition, Yeomans

    2. Relevant equations


    3. The attempt at a solution
    In the first section of this chapter,Author used this method for ising model, I know that should use the Bogoliubov inequality, taking the average in ensemble, minimizing the free energy .

    I should use the previous problem , but how? How should give ensemble on the vector spin. Am I should indicate that the free energies are equal? for equality of Hamiltonian?
    I don't have any idea at start point to indicate that 2 Hamiltonian are same.

    Appreciate any help.
     
  2. jcsd
  3. Jun 30, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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