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A spin system consists of spins that have a non-degenerate ground state and an m-fold degenerate excited state with energy ε. The spins are interacting so weakly that they be considered as independent.

The total number of spins is denoted by N, the number of spins in an excited state is n.

Analyse the system with the micro-canonical ensemble method:

a) What is the number of microstates Ω(n) pertaining to the macrostate in which n spins are excited ? Explain.
b) Calculate the number of excited spins n as a function of the temperature T.
c) Calculate the heat capacity of the system as a function of temperature.

 

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