Fluctuation-induced vortex pattern and its disordering in the fully frustratedXYmodel on a dice lattice

Abstract

A highly degenerate family of states, in which the plaquettes with the same sign of vorticity form clusters of three [proposed in Phys. Rev. B 63, 134503 (2001)] is proven to really minimize the Hamiltonian of the fully frustrated XY model on a dice lattice. The harmonic fluctuations are demonstrated to be of no consequence for the removal of the accidental degeneracy of these states, so a particular vortex pattern can be stabilized only by the anharmonic fluctuations. The structure of this pattern is found and the temperature of its disordering due to the proliferation of domain walls is estimated. The extreme smallness of the fluctuation induced free energy of domain walls leads to the anomalous prominence of the finite-size effects, which prevents the observation of vortex-pattern ordering in numerical simulations. In such a situation the loss of phase coherence may be related to the dissociation of pairs of fractional vortices with the topological charges ±1/8. In a physical situation the magnetic interactions of currents in a Josephson junction array will be a more important source for the stabilization of a particular vortex pattern then the anharmonic fluctuations.

Nature of phase transitions in the striped phase of a triangular-lattice Ising antiferromagnet

“…In the latter case the role of J k with k > 1 is played by the magnetic interactions of currents in the array [38,39]. The results of this work may also be of help for understanding the nature of phase transition(s) in the fully frustrated XY model on a honeycomb lattice [40,41], in which the fluctuation-induced vortex pattern [41] has the same structure as in Fig.…”

Spin-wave analysis of the transverse-field Ising model on the checkerboard lattice

“…This implies that the spectrum of linear excitations is defined unambiguously in the J 2 > J 1 region -this situation persists also in the isotropic case of square ice, J 1 = J 2 , for which the lowest branch of the excitation spectrum is a flat band. But this implies as well that the classical degeneracy remains unaltered in presence of harmonic quantum fluctuations, which means that only non-linear quantum fluctuations can lift the degeneracy, a situation previously encountered in a number of frustrated magnets [19][20][21][22][23][24][25] . Moreover, harmonic quantum fluctuations triggered by a sufficiently strong field are found to reverse the classical hierarchy of ordered states close to the isotropic (J 1 = J 2 ) limit, suggesting that anharmonic fluctuations might destabilize the classical order completely.…”

Correlated Phases of Bosons in the Flat Lowest Band of the Dice Lattice

“…The rich physics of these systems stems from a highly degenerate manifold of states at low energies [5], described as vortex lattices. Dynamics in this manifold is slow [6], and ordering at the lowest temperatures is determined by such subtle effects as magnetic interactions of currents [7] or anharmonic fluctuations [8].…”