Thermodynamic Behavior of Ising Model
This page is still under construction!
Intuition for what states are high/low energy and high/low entropy.
Reminder about why we care about sums of states
What do thermodynamic averages mean here? Why do we care about this?
High temperature behavior: random spins, entropy dominate
Low temperature behavior: Mostly all aligned in one direction
Remark on the puzzling symmetry breaking of low temperature phase, and the huge kinetic barrier for getting from all-up to all-down state
Remark on perturbative high-temperature or low-temperature expansions
There must be a phase transition between paramagnetic and ferromagnetic phases!
(Include a phase diagram somewhere in here too?)
Peierl's argument for the Phase Transition
Interpret as a balance between entropy and energy – the sign of the free energy
Go through argument of nucleating a droplet with surface length L…
Dimensionality matters, since there's no P.T. in one dimension.