Phase Transitions - Homework 10
Problem 10.1
Linearizing the obtained RG equations in small g at the isotropic WilsonFisher xed point u = v = w = uiso gives:
dr
dl
d(r + g)
dl
du
dl
dv
dl
dw
dl
uiso
uiso
g
2
r+
(r + 2 )2
uiso
uiso
= 2(r + g) + (n 1)
3g
2
Homework Assignment #4, Phase Transitions
Huan D. Tran
Homework Assignment #6 - Solution
Graduate student, FSU Physics Department
Section 2
We are trying to t the data of conductivity as function of temperature of the form:
(T ) = 0(n; T = 0) + mT :
(1)
W
Phase Transitions - Homework 9
Problem 9.1
In 4 theory, the following diagrams contribute to the renormalization:
Figure 2: One loop contribution to
the 4-point-function of 4 theory,
aecting the renormalization of u.
A, B, C, D, E, F are labels for the
re
1
Phase Transitions - Homework 7 - Solutions
PROBLEM 7.2
(a) In 1 dimension, the free energy (per unit cell) is given by
f (t, h) = b1 f (K(b), h(b),
where b is the scaling factor by which the lattice spacing got increased, h is the external
eld and K is
Phase Transitions - Homework 8: Solutions
Problem 8.1
(a) Any real symmetric matrix K can be diagonalized by a similarity trans
formation K = A1 T A = diag(1 , 2 , . . . , n ) where A is the transformation
matrix and the i are the eigenvalues of K. Dening
HW2 SOLUTION
1
Problem 1.
The partition function for an innite range Ising ferromagnet can be written
Z (T, h) =
J
2
1
2
dt exp N [
t2
+ ln(cosh(h + t) + ln 2] .
2J
(1)
Now, to begin computing the integral using the saddle point method (also called the me
Solutions for HW#3
Problem 3.1
S(0)
The dention of the susceptibility is (x) = h(x) where S (0) = Z 1 cfw_Sx S (0) exp (H [S (x)]) and the
sum is taken to mean a discrete sum or integral in the continuous case. We know that within the Hamiltonian the
mag
Homework Assignment #1 - Solutions
Problem 1. The rst law of thermodynamics gives:
Q(p, V, T ) = E(V, T ) + (pV ).
(1)
At constant p, the total dierential form of this law is written as:
E
V
dQ =
E
T
dV +
p,T
dT + pdV.
(2)
p,V
The specic heat Cp is dened
Phase Transitions: Homework 5 - Solution
Problem 5.1
Starting with a gas of density n. The probability of nding a particle in
innitesimal volume element V is given by P1 (V ) = nV . This implies
that the chance of nding no particle within V is given by
P0
1
HW4 SOLUTION
1) Charging energy of the droplet
To calculate energy of a charged droplet, we consider a uniformly charged sphere of radius R with the charge density
enc
being equal to = en. Using Gauss law ( S E dA = Q0 ), it is easy to show that electri