Attraction controls the entropy of fluctuations in isosceles triangular networks

TL;DR

This paper investigates how attraction influences the entropy of fluctuations in isosceles triangular networks, revealing a mechanism that determines the stable phase through entropy changes, applicable across different dimensions.

Contribution

It demonstrates that attraction can invert the stable phase by altering fluctuation entropy, using exact and numerical methods for harmonic interactions in 2D and 3D networks.

Findings

Attraction causes phase inversion via entropy change.

Exact entropy expressions for harmonic interactions are derived.

The attraction-mediated phase selection mechanism is general across dimensions.

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.