Phys (6)572 PS 6
HW due: 3/6/13, solutions out: 3/11/13
Shivam Ghosh
1
Phase-space units and the zero of entropy
(Sethna Ex. 7.3)
(a) Let us begin by considering a change in width E of the energy cont
Phys (6)562 PS 3
HW due: 2/13; Solutions out: 2/20
SHIVAM GHOSH
1
Hard discs gas and excluded volume (Sethna
Ex 3.5)
(a) To nd the allowed 2N dimensional volume in conguration space, we
remind ourselv
HW 10 solutions
Hw due 4/24/13, solutions out: 4/30/13
Shivam Ghosh
1
Sethna 11.1 and 11.2
Maxwell and van der Waals (Sethna 11.1)
Fig. 1 P V plot van der Waals, picture taken from Francois Heberts HW
Phys (6)562 Solutions 7
HW set due: 3/27, solutions out: 4/3
Shivam Ghosh
1
Ising uctuations and susceptibilities (Sethna
8.2)
The Hamiltonian for the Ising model is given by (Sethna eq. 8.1)
H=
J si
Phys (6)562 PS 4
Shivam Ghosh
Hw due: 2/20, Solutions out: 2/27
Solutions for Problem 3 and 4 have been adapted from Jim Sethnas
solutions manual
1
Invariant measures (Sethna 4.3, modied)
In this prob
Solutions HW 9
1
Equipartition for Fourier components
The probability distribution q is given to be proportional to
q = N eKq (|Xq |
2 + |X
2
q |
)/2T
(1)
where N is a normalization constant. To nd th
HW 12 solutions
HW due: 5/8/13, solutions out: 5/13/13
Shivam Ghosh
1
Decimation R.G. for the hierarchical lattice (from
Phys 653 solutions 2007)
We are to perform a decimation procedure on the hierar
Phys (6)562 PS 1
1
Random deposition I: surface growth
(a) The deposition of atoms at a site (i, j ) on the surface can be modeled as
a succession of uncorrelated random events. If the total number of
HW 8 Solutions: Phys (6)562
PS due:4/3, solutions out: 4/10
Shivam Ghosh
April 9, 2013
1
Detailed balance
Let us consider the Markov chains of Sethna chapter 8 evolving in a discrete time
t = 0, 1, .
Phys (6)562, PS 5
HW due: 2/27, solutions out: 3/6
Shivam Ghosh
1
Entropy increases: diusion (Sethna 5.10)
We need to show that the entropy S = kB (x)log(x)dx strictly increases
in time. The time deri
HW solutions PS 11
HW due: 5/1/13, solutions out: 5/8/13
Shivam Ghosh
1
Numerical critical exponents: 2D Ising model
The problem entails doing a crude estimation of the exponent which governs
the scal
Phys (6)562 PS 2
Solutions by Shivam Ghosh
PS due: 2/6/13, solutions out: 2/13
1
Random walk with correlations
(a) Correlations of the step
Given that at the i th instant in time, the step was
the exp