The classical $J_1$-$J_2$ Heisenberg model on the Kagome lattice

TL;DR

This study uses large-scale simulations to show that even small next-nearest neighbor interactions in the classical $J_1$-$J_2$ Heisenberg model on the Kagome lattice induce significant antiferromagnetic order and phase transitions, revealing complex critical behavior.

Contribution

It provides the first large-scale simulation analysis of the extended classical Heisenberg model on the Kagome lattice including $J_2$ interactions, uncovering induced order and phase transition phenomena.

Findings

Small $J_2$ induces antiferromagnetic order.

Finite-size behavior suggests phase transitions at non-zero $J_2$.

Identified two phase transitions near $J_2=0$ with different universality classes.

Abstract

Motivated by earlier simulated annealing studies and materials with large spin on the Kagome lattice, we performed large scale parallel tempering simulations on the Kagome lattice for the extended classical Heisenberg model including next nearest neighbor interactions. We find that even a small inclusion of a $J_2$ term induces anti-ferromagnetic order which prevails in the thermodynamic limit. The magnitude of this effect is surprising. While at $J_2=0$ the finite-size behaviour does not suggest a phase-transition, at other points the numerical result is consistent with one. Close to $J_2=0$ and for a positive sign of $J_2$ two subsequent phase-transitions/crossovers are found, one of them connecting to the crossover for the $J_2=0$ case, shedding light to the pure case. The universality classes of the transitions were explored.