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2. Alugnetic wsceptibility (-) Lise the petition function to fill an exact expression for the longitetization and the susceptibility X E JAPANS as a function of temperature and magnetic field for the model system of magnetic moments in a magnetic field. The result for the magnetization is N - non tanti(ontfr/c), as derived in (46) by another method. Here is the particle + Chapter Ii Rolemaan Distribution and Helmhof: Free Energy 0.8 log 2 0.6 o(1) 0.4 0.2 OS 1.5 2.0 10 Tit Fleure 3.11 Entropy of a two-state system as a function aft/. Notice that alt) - log2 as : -+ . סן 03 0.5 1.5 2.0 10 MB Figure 3.12 Plot of the total magnetic moment as a function of m'. Notice that allow Bit the montent is a liscar function of ms, but al high at the monacattends to suurute. concascation. The result is portal in Figure 3.12. (b) Find the free energy and express the result as a function only of randalie parameter x = M() Show that the susceptibility is z * in the limit 13 « t. 3. free energy of a harmonic oscillator. A one-dimensionat hamonic oscil- Tator has an infinite series of equally spaced energy states, wittig, = shu, where