224 Problem3 d Solutiom on thermodynamic^ d Statistical Mechanics
Solution:
(a) The partition function is
J
= empHIkT = sinh
m=- J
(b) The average magnetization is
- M=-(g)T=NkT(&lni)
T
= 2 [(2J + 1) coth (2.7 + 1)- - coth
2 [ 2kT 2kT
(c) When kT >> pH, using
cothxa?(l+%), 2 for x<1
we get
M - w -NJ(J^1 + 1)- P2 H
3 kT
2058
Two dipoles, with dipole moments MI and M2, are held apart at a
separation R, only the orientations of the moments being free. They are in
thermal equilibrium with the environment at temperature T. Compute the
mean force F between the dipoles for the high temperature limit __
kT R3
- The system is to be treated classically.
Remark: The potential energy between two dipoles is:
MlM2 <<
(3(M1 .R)(M2 .R) - (MI .M2)R2)
4= R5
(Princeton)
Solution:
Taking the z-axis along the line connecting'M1 and M2, we hatre
[2 cos 81 cos e2 - sin 81 sin 82 cos(pl - p2)].
4=- Ml M2
R3