- #1
asynja
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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.
Help? Thnx in advance.
(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.
Help? Thnx in advance.
