Word Count : 192

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Consider a single free spin \$J=S=\tfrac12\$ with magnetic moment \$\mu\_z=g\mu\_B m\$ in a uniform magnetic field \$B\$ (with \$m=\pm\tfrac12\$). The energy of the two Zeeman levels is \$E\_{m}=-\mu\_z B=-g\mu\_B m B\$, so explicitly \$E\_{+1/2}=-\tfrac{1}{2}g\mu\_B B\$ and \$E\_{-1/2}=+\tfrac{1}{2}g\mu\_B B\$. Put \$\beta\equiv 1/(k\_B T)\$. The partition function for one spin ________ _________ ________ _____ ___ _____ _____.
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