(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A ‘lattice gas’ consists of a lattice of N sites. Each of these sites can be empty, in which

case its energy is zero, or occupied by one particle, in which case its energy is e. Each particle

has a magnetic moment of magnitude μ which in the presence of an applied magnetic field

B, can adopt two orientations (parallel or anti-parallel to the field). Evaluate the mean energy

and mean magnetic moment of the system assuming that the particles are not interacting with

each other.

2. Relevant equations

[tex]Z=\sum_r e^{-\beta E_r}[/tex]

[tex]p_r=\frac{1}{Z}e^{-\beta E_r}[/tex]

For a system of n defects in a system of N sites,

[tex]\frac{n}{N}=\frac{1}{e^{\beta \epsilon}+1}[/tex]

where ε is the energy associated with the defect

Mean energy,

[tex]\bar{E}=\frac{\partial \ln{Z}}{\partial\beta}[/tex]

3. The attempt at a solution

My problem is that I'm not sure whether there are three separate states for each site, or are there only 2 energy states and the schottky's defect must be considered separately.

If I consider that there are 3 possible states, then the possible energies are

[tex]\epsilon+\mu\beta,0\ \textrm{and}\ \epsilon-\mu\beta[/tex]

But if this is not right, then I'm not sure how to go about on this question.

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# Schottky's defect

Can you offer guidance or do you also need help?

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