Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach

TL;DR

This paper demonstrates that the classical kagome antiferromagnet exhibits long-range order of the  type, using an effective Hamiltonian approach to analyze soft mode correlations and discrete state interactions.

Contribution

It introduces an effective Hamiltonian framework to analytically estimate soft mode correlations and establish long-range order in the kagome antiferromagnet.

Findings

Long-range  order confirmed

Effective Hamiltonian derived for soft modes

Analytical estimates of correlations obtained

Abstract

Following Huse and Rutenberg [Phys. Rev. B 45, 7536 (1992)], I argue the classical Heisenberg antiferromagnet on the kagom\'e lattice has long-range spin order of the $\sqrt{3}\times\sqrt{3}$ type (modulo gradual orientation fluctuations of the spins' plane). I start from the effective quartic Hamiltonian for the soft (out of plane) spin fluctuation modes, and treat as a perturbation those terms which depend on the discrete coplanar state. Soft mode correlations, which become the coefficients of a discrete effective Hamiltonian, are estimated analytically.