We describe a phase transition that gives rise to structurally non-trivial states in a two-
dimensional ordered network of particles connected by harmonic bonds. Monte Carlo
simulations reveal that the network supports, apart from the homogeneous phase, a number
of heterogeneous “pleated” phases, which can be stabilised by an external field. This field is
conjugate to a global collective variable quantifying “non-affineness,” ie, the deviation of
local particle displacements from local affine deformation. In the pleated phase, stress is …

We describe a phase transition that gives rise to structurally non-trivial states in a two-
dimensional ordered network of particles connected by harmonic bonds. Monte Carlo
simulations reveal that the network supports, apart from the homogeneous phase, a number
of heterogeneous “pleated” phases, which can be stabilised by an external field. This field is
conjugate to a global collective variable quantifying “non-affineness”, ie the deviation of
local particle displacements from local affine deformation. In the pleated phase, stress is …