Rudolf Peierls introduced an argument explaining how a two-dimensional Ising model can sustain magnetic order at low temperature. A reversed island of spins has a boundary whose energy cost grows with its length. The number of possible boundaries also grows, but sufficiently low temperature suppresses their Boltzmann weights strongly enough for order to survive. The Peierls argument makes the competition between energy and the number of fluctuations explicit, helping explain why dimensionality changes collective magnetic behavior.[ref]
On Ising's model of ferromagnetism by Rudolf Peierls. Proceedings of the Cambridge Philosophical Society 32, 477–481 (1936), low-temperature contour argument
Portrait of Rudolf Peierls
. GFHund; photograph from Friedrich Hund's estate, prepared by Gerhard Hund. CC BY 3.0, via Wikimedia Commons. Source.
