Hand In Exercise 4
Due at the problem class, Thursday, Oct 13th at the beginning of the problem class (11:30).
Hard spheres Phase Diagram
A very accurate expression for the free energy of N hard spheres of diameter at density
= N/V at temperature T is du

Advanced Statistical Physics
L. Filion and R. van Roij
2
Introductory Remarks
This is fairly new version of lecture notes for the course Advanced Statistical Mechanics, and will be
used in the academic year 2016 - 2017. While care has been taken to avoid

Review
Review: Overview of Course
Review of thermodynamics and statistical
mechanics
Phase space & Classical Ensemble Theory
Phase behaviour
Chemical equilibria
An exact solution: the 1d Ising model
Mean field theory
Landau theory
Low Density Liquids (Vir

Hand In Exercise 3
Due at the problem class, Tuesday, October 4th at 13:30.
Demixing transition
Consider a binary lattice gas on a square lattice: there are two species labeled 1 and 2, with
densities 1 and 2 . Particles do not interact with any of the ot

Hand In Exercise 2
Due at the problem class, Tuesday, Sept 27th at 13:30.
Let A and B be two dierent states of a molecule. Now assume that is the energy dierence
between states A and B. Assume that the system consists of N of these molecules in a volume
V

Problems Week 4
1. Van der Waals Equation of State
The van der Waals equation of state p() is given by
N kB T
a2
V Nb
p() =
(19.1)
where N is the number of particles, V is the volume, kB is Boltzmanns constant, is the
density, p is the pressure, and a,b

Problems Set 2
1. Reading Assignment
Read (and make sure you can understand and re-derive) the sections in the lecture notes on the
equipartition theorem (Section 3.4) and chemical equilibrium (Chapter 5).
2. Classical Ideal Gas
Calculate the grand-canoni

Problems Week 3
1. Phase diagram
A theorist develops an approximate theory to calculate the free energy of the system. The free
energy she nds, is shown in Figure 18.1 for four dierent temperatures. Note that here she has
plotted F/V as a function of the

Problems Week 1
1. Three state system
Consider a system of N identical, non-interacting particles, each which has three possible energy
levels: E1 = 2/3, E2 = E3 = /3.
(a) What do the states in this system look like?
(b) Write down the canonical partition

Hand In Exercise 1
September 28, 2016
(a) The partition function of a single spin:
Q1 = eH + eH = 2 cosh(H).
The probabilities of spin up (p+ ) and spin down (p ):
p+
p
eH
,
eH + eH
eH
= H
.
e
+ eH
=
(b) The average number of spin up (down) particles is s

Sample Midterm Exam Questions
Formula Sheet (will also be used in 2016)
The canonical partition function of a classical thermodynamic system of N identical
particles in a volume V aR temperature T with Hamiltonian H() is written as
Z(N, V, T ) = 1/(N !h3