Monte Carlo study of degenerate groundstates and residual entropy in a frustrated honeycomb lattice Ising model

TL;DR

This paper investigates the residual entropy and ground states of a frustrated honeycomb Ising model using Monte Carlo methods, introducing a novel non-local algorithm to efficiently sample degenerate states and explore effects of perturbations.

Contribution

It develops a non-local 'chain-flip' Monte Carlo algorithm to effectively sample degenerate ground states in a frustrated Ising model, addressing limitations of traditional methods.

Findings

Residual entropy scales with system size N

Magnetic field induces non-extensive and extensive residual entropy states

The chain-flip algorithm enables discovery of ordered ground states

Abstract

We study a classical fully-frustrated honeycomb lattice Ising model using Markov chain Monte Carlo methods and exact calculations . The Hamiltonian realizes a degenerate ground state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one frustrated bond, with an extensive residual entropy that grows as the number of spins N. Traditional single-spin flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers. We develop a non-local "chain-flip" algorithm that solves this problem, and demonstrate its effectiveness on the Ising Hamiltonian with and without perturbative interactions. The two perturbations considered are a slightly weakened bond, and an external magnetic field h. For some cases, the chain-flip move is necessary for the simulation to find an ordered ground state. In the case of the magnetic field, two magnetized ground states with non-extensive entropy are found, and two special values of h exist where the residual entropy again becomes extensive, scaling proportional to N ln phi, where phi is the golden ratio.