PY 410, Statistical and Thermal Physics, Spring 2010

Homework 1 (Due Feb. 2nd), problems from Reif: 1.1; 1.4 (analyze the answer at large N), 1.5, 1.9, 1.10, 1.12, 1.14. Solution

Homework 2 (Due Feb. 9th), problems from Reif: 1.16; 1.17, 1.18, 1.23; *1.26, *1.28 (for the last two problems you need to read Sec. 1.10) Solution

Homework 3 (Due Feb. 18th), problems from Reif: 2.1; 2.2, 2.4, 2.8; 2.10 Solution

Lecture8       Additional reading: Chapter 3 from Reif.

Homework 4 (Due Feb. 23rd), problems from Reif: 3.1, 3.3, 3.4.

Repeat the problem considered in the notes but for spin 1 particles. I.e. assume that we have a system of large number N of noninteracting particles described by the Hamiltonian:
, where .
Find the approximate expressions for the density of states  and then find the temperature as a function of the energy and the magnetic field. Invert this relation and express energy in the system as the function of temperature. Show that your result is consistent with the Boltzmann distribution where the probabilities of spins to be in one of the three possible states are

Hint: number of configurations such that .spins have magnetization 1, .- have magnetization 0, and .have magnetization -1 is given by the polynomial distribution

where
. Because the total energy is fixed  we have an additional constraint. Using Stirling’s approximation maximize the number of configurations with respect to remaining variable. This is approximately  you need to find. Solution