At absolute zero, a two-dimensional array of identical interacting particles crystallizes into a hexagonal close-packed lattice. But if the particles are warmed even a little, long-wavelength fluctuations will destroy the lattice’s perfect translational symmetry. Orientational order persists, however. Although the particles may no longer be equally spaced, they’ll still line up in crisscrossing diagonal rows.

What happens to a 2D crystal as the temperature increases further has interested physicists for decades. Eventually, of course, the crystal melts. But in between, its more or less uniform orientational order begins to crumble and a topologically distinct state, a hexatic state, appears: Pairs of point defects called dislocations sprout and spread, fragmenting the crystal into patches of local orientational order demarcated by defects called disclinations.

That 2D melting proceeds via a hexatic state was predicted in 1978 by Bertrand Halperin and David Nelson 1 and observed 20 years later in a system of...

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