The Boltzmann factors of the states of the system, the partition function, probabilities of finding the dipoles parallel and antiparallel and plot of these probabilities as a function of k T ∈ , plot of average energy of the system and the temperatures at which one is more likely to find both dipoles pointing up than to find one up and one down.

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Chapter 8.2, Problem 17P

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The Boltzmann factors of the states of the system, the partition function, probabilities of finding the dipoles parallel and antiparallel and plot of these probabilities as a function of kT∈ , plot of average energy of the system and the temperatures at which one is more likely to find both dipoles pointing up than to find one up and one down.

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Consider an Ising model of just two elementary dipoles, whose mutual interaction energy is ± E. Enumerate the states of this system and write down their Boltzmann factors. Calculate the partition function. Find the probabilities of finding the dipoles parallel and antiparallel , and plot these probabilities as a function of kT/ E. Also calculate and plot the average energy of the system. At what temperatures are you more likely to find both dipoles pointing up than to find one up and one down?

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