PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #7
(1) Consider the ferromagnetic XY model, with
H=
i<j
Jij cos(i j ) H
cos i .
i
Dening zi exp(ii ), write zi = zi + zi with
zi = m ei .
(a) Assuming H > 0, what should you take for ?
(b) Making this choic

PHYSICS 210A : STATISTICAL PHYSICS
HW ASSIGNMENT #1 SOLUTIONS
(1) Prove that for x 0 and y 0 that
(x y) (ln x ln y) 0 .
Solution: Trivial. Both f (x) = x and g(x) = ln x are strictly increasing functions on the
interval (0, ). Hence ln x < ln y if 0 < x <

PHYSICS 210A : STATISTICAL PHYSICS
FINAL EXAMINATION
(1) Consider a lattice of noninteracting spin dimers, where the dimer Hamiltonian is
H = H H K ,
where H and H are magnetic elds acting on the and spins, respectively. Each spin
is a two-state Ising var

PHYSICS 140A : STATISTICAL PHYSICS
HW ASSIGNMENT #5 SOLUTIONS
(1) Consider a modied version of the Kac ring model where each spin now exists in one
of three states: A, B, or C. The ippers rotate the internal states cyclically: ABCA.
(a) What is the Poinca

PHY 203: Solutions to Problem Set 10
January 7, 2007
1
Problem 11.10
This question asks you to consider a body rotating about a xed diameter (i.e.
external forces are applied to hold the axis of rotation in place), but with a
moment of inertia that change

PHY 203: Solutions to Problem Set 7
November 30, 2006
1
Problem 13.4
In this problem we are asked to solve for the motion of a string with given initial
conditions. We start from the wave equation:
2
2
=T 2,
t2
x
(1)
where is the transverse displacement o

Physics 123 Midterm Exam Spring 2005 Solutions
1. In terms of its angular frequency , the period T of a simple harmonic oscillator is
2
a. T =
2. When the position of an oscillating particle is x = A cost , its velocity v is
c. v = dx/dt =-A sin t
3. If F

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MULTIPLE CHOICE. Choose the o ne a lternative t hat best completes the statement o r a nswers the questi

1
Outline of solutions to Homework 5
Problem 7.1: a) We set the voltage of the inner spherical shell to be V and the potential of the outer one to be
0, so the voltage dierence is V as required. By symmetry, the current density is directed radially outwar

1
Outline of solutions to Homework 6
Problem 4.22: Since the cylinder is a uniform dielectric, the electrostatic potential obeys Laplaces equation inside
and outside. From experience, we know the solution inside corresponds to a uniform electric eld, so V