Order-by-disorder in the antiferromagnetic Ising model on an elastic triangular lattice

TL;DR

This paper investigates how entropy-driven effects, specifically order-by-disorder, influence the ground state and finite-temperature behavior of the antiferromagnetic Ising model on a deformable triangular lattice, revealing a partially disordered ground state and glassy dynamics.

Contribution

It provides an exact microscopic calculation of displacements and demonstrates entropy's role in lifting degeneracy, leading to a partially disordered ground state in a frustrated system.

Findings

Identifies a partially disordered ground state with zigzagging stripes.

Shows each configuration has a unique phonon spectrum and entropy.

Finds the system exhibits glassy behavior due to energy barriers.

Abstract

Geometrically frustrated materials have a ground-state degeneracy that may be lifted by subtle effects, such as higher order interactions causing small energetic preferences for ordered structures. Alternatively, ordering may result from entropic differences between configurations in an effect termed order-by-disorder. Motivated by recent experiments in a frustrated colloidal system in which ordering is suspected to result from entropy, we consider in this paper, the antiferromagnetic Ising model on a deformable triangular lattice. We calculate the displacements exactly at the microscopic level, and contrary to previous studies, find a partially disordered ground state of randomly zigzagging stripes. Each such configuration is deformed differently and thus has a unique phonon spectrum with distinct entropy, thus lifting the degeneracy at finite temperature. Nonetheless, due to the free-energy barriers between the ground-state configurations, the system falls into a disordered glassy state.