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Binvestigator

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## Homework Statement

The mean-field equation for the three-state Potts model H= -J∑δ

_{σi}δ

_{σj}can be derived as follows using this:

a) show that H is equivalent to -J∑

**S**

_{i}.

**S**

_{j}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

## Homework Equations

## 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.