Blundell Thermal Physics · Problem 20.6

The partition function

Physics — Statistical Mechanics · magnetic-susceptibility-four-level

Problem

A certain magnetic system contains

n

independent molecules per unit volume, each of which has four energy levels given by

0,\ \Delta - g\mu_B B,\ \Delta,\ \Delta + g\mu_B B

(

g

is a constant). Write down the partition function, compute the Helmholtz function and hence compute the magnetization

M

. Hence show that the magnetic susceptibility

\chi

is given by

\chi = \lim_{B\to 0} \frac{\mu_0 M}{B} = \frac{2n\mu_0 g^2\mu_B^2}{k_B T(3 + e^{\Delta/k_B T})}. \tag{20.55}