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A statistical system is composed of N particles with spin 1 2 , immersed in a...

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Physics

A statistical system is composed of N particles with spin 1 2 ,immersed in a magnetic field H. The particles are fixed in theirpositions and possess a magnetic moment µ. The Hamiltonian of sucha system is H = −µH X N i=1 σi where σi = ±1

(a) Given that the separation between the spins in the latticeis larger than their de Broglie wavelength, should the spins betreated as distinguishable or indistinguishable particles?

(b) Write down the canonical partition function, QN , for the Nparticles.

(c) Determine the total energy for this system at an arbitrarytemperature, T.

(d) Magnetization is defined as the M = µ(N+ − N−) where N+ andN− are the average number of up and down spins, respectively.Determine M for a given temperature T.

(e) The susceptibility is defined as χ = ∂M ∂H T Find the smallmagnetic field limit of the susceptibility

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