# Peierl's Proof on Spontaneous Magnetization

How to modify Peierls proof to show that, for the Ising model on the hexagonal lattice with nearest neighbor ferromagnetic coupling $J$, at low temperatures there is a spontaneous magnetization?

• The proof is identical, what would you change? The only (mostly trivial) change concerns the combinatorics of contours, i.e., getting an upper bound on the number of contours of length $\ell$ surrounding a given vertex. But this is done in the same way as on the square lattice, only the constants change. – Yvan Velenik Sep 18 '17 at 7:28