Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem

TL;DR

This paper explores the transition from paramagnetism to ferromagnetism in flat-band systems using a Hubbard model on the Tasaki lattice, revealing a complex percolation problem with exact solutions in 1D and numerical methods in 2D.

Contribution

It introduces a novel geometric percolation framework for analyzing ferromagnetism in flat-band systems and provides exact and numerical solutions for different dimensions.

Findings

Exact solution for 1D case

First-order transition in 2D

Ferromagnetic phase persists beyond uncorrelated percolation point

Abstract

We investigate the location and nature of the para-ferro transition of interacting electrons in dispersionless bands using the example of the Hubbard model on the Tasaki lattice. This case can be analyzed as a geometric site-percolation problem where different configurations appear with nontrivial weights. We provide a complete exact solution for the 1D case and develop a numerical algorithm for the 2D case. In two dimensions the paramagnetic phase persists beyond the uncorrelated percolation point, and the grand-canonical transition is via a first-order jump to an unsaturated ferromagnetic phase.