TL;DR
This paper introduces a two-dimensional Ising spin configuration with a flat scattering pattern, revealing a form of perfect order underlying apparent amorphousness, and explores its temperature-dependent ordering transitions.
Contribution
It presents a novel amorphous spin configuration with underlying order and analyzes its finite temperature phase transitions, bridging amorphous and ordered states.
Findings
Scattering pattern is flat despite underlying order
Ground state achieved with finite-range interactions
Ordering transitions occur at larger length scales with temperature
Abstract
A solid is typically deemed amorphous when there are no Bragg peaks in its diffraction pattern. We discuss a two dimensional configuration of Ising spins with an autocorrelation function which vanishes at all nonzero distances, so that its scattering pattern is flat. This configuration is a ground state of a Hamiltonian with deterministic, translationally-invariant and finite range interactions. Despite ostensibly being amorphous, this configuration has perfect underlying order. The finite temperature behavior of this model exhibits ordering transitions at successively larger length scales.
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