(Solution) - Find the equilibrium value at temperature of the fractional -(2025 Original AI-Free Solution)

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Find the equilibrium value at temperature ? of the fractional magnetization

M Nm = 2< s >/N

Of the system of N spins each of magnetic moment m in a magnetic field B. The spin excess is 2s. take the entopy as the logarthithm of the multiplicity g(N,s) as given in

?(s) ? log g(N, 0) ? 2s2/N (40)

for |s| << N.

?(U) = ?0 ? U2/2m2B2N (41)

with ?0 = log g(N, 0). Further, show that 1/? = ?U/m2B2N, where U denotes < U >, the thermal average energy.