A class of classical lattice models on Z^d (d≥2) with non-negative integer on-site states and nearest-neighbor interactions exhibits long-range checkerboard order at arbitrarily high temperatures via a purely entropic mechanism, proven using Pirogov-Sinai theory with a Peierls bound.
Popov, and Tin Sulejmanpasic
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Order by disorder up to arbitrarily high temperature
A class of classical lattice models on Z^d (d≥2) with non-negative integer on-site states and nearest-neighbor interactions exhibits long-range checkerboard order at arbitrarily high temperatures via a purely entropic mechanism, proven using Pirogov-Sinai theory with a Peierls bound.