Ground states of the Ising model at fixed magnetization on a triangular ladder with three-spin interactions

TL;DR

This paper exactly determines the ground states of a triangular ladder Ising model with three-spin interactions at fixed magnetization, revealing diverse phases and phase transitions through linear programming.

Contribution

It introduces a novel linear programming approach to exactly solve the ground states of the model at fixed magnetization, including phase diagram construction.

Findings

Identified three types of ground states: periodic, phase-separated, and aperiodic.

Constructed the phase diagram for arbitrary fixed magnetization.

Found that free magnetization states are mostly periodic with specific magnetization values.

Abstract

We study the Ising model at fixed magnetization on a triangular ladder with three-spin interactions. By recasting the ground-state determination as a linear programming (LP) problem, we solve it exactly using standard LP techniques. We construct the phase diagram for arbitrary fixed magnetization and identify three types of ground states: periodic, phase-separated, and ordered but aperiodic. When magnetization is treated as a free parameter, the ground state adopts only periodic configurations with the average magnetization per site $0$, $\pm 1/3$ or $\pm 1$, except for the phase boundaries.