Phase transitions, order by disorder and finite entropy in the Ising antiferromagnetic bilayer honeycomb lattice

TL;DR

This paper investigates the complex phase behavior of the Ising antiferromagnetic bilayer honeycomb lattice, revealing finite entropy phases, diverse phase transitions, and order-by-disorder phenomena through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of the phase diagram, including exact zero-temperature results and finite-temperature properties using Bethe lattice and Monte Carlo simulations.

Findings

Finite entropy phases at zero temperature.

Presence of first and second order phase transitions.

Order-by-disorder state selection observed.

Abstract

We present an analytical and numerical study of the Ising model on a bilayer honeycomb lattice including interlayer frustration and coupling with an external magnetic field. First, we discuss the exact $T=0$ phase diagram, where we find finite entropy phases for different magnetisations. Then, we study the magnetic properties of the system at finite temperature using complementary analytical techniques (Bethe lattice), and two types of Monte-Carlo algorithms (Metropolis and Wang-Landau). We characterize the phase transitions and discuss the phase diagrams. The system presents a rich phenomenology: there are first and second order transitions, low-temperature phases with extensive degeneracy, and order-by-disorder state selection.