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1. Consider a model of N localized magnetic ions, given by the spin Hamiltonian N H = D> S;, j=1 where the spin variable S; may assume the values -1, 0, or +1, for all j (see exercise 6 of Chapter 2). Given the total energy E, use the expression for the number of accessible microstates, N (E, N), to obtain the entropy per particle, s = s (u), where u = E/N. Obtain an expression for the specific heat c in terms of the temperature T. Sketch a graph of c versus T. Check the existence of a broad maximum associated with the Schottky effect. Write an expression for the entropy as a function of tem- perature. What are the limiting values of the entropy for T → 0 and T → 0? *** The number of accessible microscopic states, N (E, N), has already been calculated in exercise 6 of Chapter 2. The entropy per magnetic ion is given by 1 8 = s (u) = kB lim In Ω (E, N), - N

1. Consider a model of N localized magnetic ions, given by the spin Hamiltonian N H = D> S;, j=1 where the spin variable S; may assume the values -1, 0, or +1, for all j (see exercise 6 of Chapter 2). Given the total energy E, use the expression for the number of accessible microstates, N (E, N), to obtain the entropy per particle, s = s (u), where u = E/N. Obtain an expression for the specific heat c in terms of the temperature T. Sketch a graph of c versus T. Check the existence of a broad maximum associated with the Schottky effect. Write an expression for the entropy as a function of tem- perature. What are the limiting values of the entropy for T → 0 and T → 0? *** The number of accessible microscopic states, N (E, N), has already been calculated in exercise 6 of Chapter 2. The entropy per magnetic ion is given by 1 8 = s (u) = kB lim In Ω (E, N), - N

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1. Consider a model of N localized magnetic ions, given by the spin Hamiltonian N H = DS}, j=1 where the spin variable S; may assume the values -1, 0, or +1, for all j (see exercise 6 of Chapter 2). Given the total energy E, use the expression for the number of accessible microstates, 2 (E, N), to obtain the entropy per particle, s = s(u), where u = E/N. Obtain an expression for the specific heat c in terms of the temperature T. Sketch a graph of c versus T. Check the existence of a broad maximum associated with the Schottky effect. Write an expression for the entropy as a function of tem- perature. What are the limiting values of the entropy for T → 0 and T → x? *** The number of accessible microscopic states, 2(E, N), has already been calculated in exercise 6 of Chapter 2. The entropy per magnetic ion is given by 1 s = s (u) = kB lim lnΩ (E, N), N
Transcribed Image Text:1. Consider a model of N localized magnetic ions, given by the spin Hamiltonian N H = DS}, j=1 where the spin variable S; may assume the values -1, 0, or +1, for all j (see exercise 6 of Chapter 2). Given the total energy E, use the expression for the number of accessible microstates, 2 (E, N), to obtain the entropy per particle, s = s(u), where u = E/N. Obtain an expression for the specific heat c in terms of the temperature T. Sketch a graph of c versus T. Check the existence of a broad maximum associated with the Schottky effect. Write an expression for the entropy as a function of tem- perature. What are the limiting values of the entropy for T → 0 and T → x? *** The number of accessible microscopic states, 2(E, N), has already been calculated in exercise 6 of Chapter 2. The entropy per magnetic ion is given by 1 s = s (u) = kB lim lnΩ (E, N), N
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