Long-range order in the classical kagome antiferromagnet: Effective Hamiltonian approach

Abstract

Following Huse and Rutenberg [Phys. Rev. B 45, 7536 (1992)], I argue the classical Heisenberg antiferromagnet on the kagome lattice has long-range spin order of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ type in the limit of zero temperature. 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 expectations become the coefficients of a discrete effective Hamiltonian, which (after a coarse graining) has the sign favoring a locking transition in the interface representation of the discrete model.