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Abstract
We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of the stable phase by changing the entropy of fluctuations around the ground-state configurations. By using a real-space shell-expansion method, we compute the exact expression of the entropy for harmonic interactions, while for repulsive harmonic interactions we obtain the entropy arising from a limited subset of the system by numerical integration. We compare these results with a three-dimensional triangular-network model, which shows the same attraction-mediated selection mechanism of the stable phase, and conclude that this effect is general with respect to the dimensionality of the system.
Highlights
Geometrically-constrained systems may show peculiar features compared to their unconstrained counterparts
Increasing temperature above zero, the degeneracy is removed through the order-by-disorder effect and we find the straight-stripes phase to be selected for particles linked with harmonic interactions, while the bent-stripes phase is more stable if only the repulsive component of the harmonic inter-particle potential is considerd
We studied a 2D triangular-network model composed of particles interacting through harmonic or repulsive harmonic springs
Summary
Geometrically-constrained systems may show peculiar features compared to their unconstrained counterparts. Straight and zigzagging stripes are the only configurations corresponding to a 2D network of isosceles triangles which can tile the plane [9] This geometric mechanism underlying the ground state of the buckled colloidal system composed of straight or zigzagging stripes, has been realised, experimentally by packing a granular system in a container under the effect of gravity [22,23], and theoretically with spins starting from the Wannier antiferromagnetic Ising model on a triangular lattice [21] by allowing for the lattice to elastically deform [24,25]. This result suggests that the inversion of the stable phase by adding attraction to repulsively-interacting particles in triangular networks is a general mechanism, irrespective of the dimensionality of the system
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