# Homework Help: Statistical Thermodynamics - Help Wanted

1. Feb 16, 2010

### asynja

Statistical Thermodynamics - Help Wanted :(

(My translation skills sucks, I hope it is understandable.)

Three spins, placed at vertices of an equilateral triangle, are put in the external magnetic field with density B. Hamiltonian of the system:
$$H = -J \sum_{<i,j>} s_{i} s_{j} - \gamma \hbar B \sum_{i=1}^3 s_{i}$$

where first sum runs over pairs of the nearest-neighbour spins and describes interactions between them, and the second sum represents spin interaction with external field; $$s_{i}$$ can take values between +1/2 and -1/2. Sketch possible states of the system and calculate the partition function! How much is the magnetic susceptibility of this triplet of spins system at T=300K ?
Other data: $$J = 0.02 eV \gamma = e_{0}/m$$ , where $$e_{0}$$ and $$m$$ are electron charge and mass. Volume, taken by this triplet of spins is $$0.1 nm^3$$

My attempt of the solution was so unsuccessful that isn't worth wasting time writing it in latex. The problem is a form of Ising model; at class we did one problem of finding Z in 1D and much simpler hamiltonian. I thought I kind of understood it then, but it doesn't help me much with this problem.

2. Feb 17, 2010

### Physics Monkey

Re: Statistical Thermodynamics - Help Wanted :(

Hi asynja,

I'm not sure what the point of this problem is exactly, but the system is simple enough with only 2^3 = 8 states that you can list all the energies for computing the partition function explicitly. Is this how you're approaching the problem?

There is also a trick for rewriting the interaction term that makes the problem easier.