Find the equilibrium value at temperature τ of the fractional

[PhysicsGente]

Homework Statement

Find the equilibrium value at temperature τ 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 entropy as the logarithm of the multiplicty g(N,s) where

σ(s) ≈ σo − (2s^2)/N

where
σo = ln(g(N,0))
and g is the multiplicity function.

Homework Equations

The Attempt at a Solution

I don't understand what I'm being asked. What do they mean by the equilibrium value?

 

[AvroArrow]

Are they asking for the equilibrium magnetization, i.e., the value of M at equilibrium? If so, then I believe the equation should be something like:M(τ) = 2sNm/g(N,s)