Consider a single large two-state paramagnet. Here the multiplicity function is very sharply peaked about N↑ = N / 2. In this problem, you will need Stirling's approximation: lnN! = NlnN - N + ln√2πN and the Taylor expansion of the natural log to second order ln(1 + ε) ≈ ε -ε2 / 2. a) Use Stirling's approximation to estimate the height of the peak in the multiplicity function.
b) How wide is the peak in the multiplicity function?