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The Ising model and the Boltzmann distribution

Draft. Outline only. Write the post under these headings.
The phase transition, simulated. Mean absolute magnetisation of a 24×24 Ising lattice against temperature (checkerboard Gibbs sampling, 400 sweeps per point; bars show ±1 s.d.). The dashed line is the exact critical temperature $T_c \approx 2.269$.

Outline

  1. The Boltzmann distribution: why $p(s) \propto e^{-E(s)/T}$
  2. Gibbs sampling one spin at a time
  3. Watching order appear below $T_c$
  4. What this has to do with graphical models and SBMs