Monte Carlo investigation of the Ising model
Tobin Fricke December 2006
The Ising Model
The Ising Model is a simple model of a solid that exhibits a phase transition resembling ferromagnetism. In this model, a spin direction is assigned to each vertex o
5600 Miscellaneous Thermodynamics
Derivation of the adiabatic equation of state for an ideal gas
Consider an ideal gas of N particles in a volume V in equilibrium at a temperature T .
The mention of an ideal gas should immediately bring to min
Grand partition function
Recapitulate the result of the derivation done in the elcture and in the text.
Consider a system in a given microstate r with energy r and number of particle
Nr of a system in thermal and diusive equilibrium with a reservoir. The
Work and heat: Supplement to Chapter 8
You should recognize or remember boxed equations and their meaning.
Thermodynamics deals with equilibrium states and transformations between them.
The external forces applied to a body can do work on it, which is det
Comments on thermodynamics
Remember that asides can be neglected for exams but can be useful and important.
Parameters that have values in a composite system equal to the sum of the values
in each of its macroscopic subsystems are called extensive paramet
Dene chemical potential1 using the idea of diusive equilibrium. Follow the
same argument as that for temperature. When two systems are in equilibrium with
respect to the exchange of energy maximizing the entropy (the two systems considered
Free Energy in Statistical Physics
Random notes on the useage of the free energy in statistical
physics and inference. Taken from Davids book Chapter 31
on Ising models, Radford Neals review of MCMC methods,
and Yedidia, Fre
Chapter 7 Quantum Statistics
Problem 7.3. Neglecting both spin (which cancels out of the nal result)'and the excited
states of the hydrogen atom (which contribute negligibly even at 10,000 K), this system
has just two states:
unoccupied: E =: 0
We used the Gibbs denition of entropy that uses the probability pj of the occurrence of each of the microstates of a system,
S = kB
pj ln(pj )
where the sum is over all microstates. Claude Shannon introduced a similar denition