Antiferromagnetic Long-Range Order in a Lattice Fermion Model

TL;DR

This paper proves the existence of antiferromagnetic long-range order in a 3D lattice fermion model with Weyl dispersion, using reflection positivity to establish phase transition at low temperatures in strong coupling.

Contribution

It introduces a new lattice fermion model with Weyl dispersion and rigorously proves antiferromagnetic long-range order using reflection positivity.

Findings

Antiferromagnetic long-range order exists at low temperatures.

Reflection positivity is established for the model.

Order persists in the strong coupling regime.

Abstract

We study a lattice fermion model with antiferromagnetic interactions on the three-dimensional cubic lattice. The hopping term of the Hamiltonian has a Weyl-type dispersion. We prove that the model has reflection positivity. Moreover, by relying on the property, we prove the existence of the antiferromagnetic long-range order at low temperatures in a strong coupling regime.