Emergent Potts Order In The Kagome J(1 )- J(3 )Heisenberg Model

Motivated by the physical properties of vesignieite BaCu3V2O8(OH)(2), we study the J(1)-J(3) Heisenberg model on the kagome lattice, which is proposed to describe this compound for J(1)<0 and J(3)>>vertical bar J(1)vertical bar. The nature of the classical ground state and the possible phase transitions are investigated through analytical calculations and parallel tempering Monte Carlo simulations. For J(1)<0 and J(3)>1+root 5/4 vertical bar J(1)vertical bar, the ground states are not all related by Hamiltonian symmetry. Order appears at low temperature via the order by disorder mechanism, favoring collinear configurations and leading to an emergent q = 4 Potts parameter, that induces a finite temperature phase transition. For J(3) between 1/4 vertical bar J(1)vertical bar and 1+root 5/4 vertical bar J(1)vertical bar, the ground state goes through a succession of semispiral states, possibly giving rise to multiple phase transitions at low temperatures. The effects of quantum fluctuations are studied through linear spin-wave approximation and high-temperature expansions of the S = 1/2 model.