5 research outputs found
Collective Excitations and Stability of the Excitonic Phase in the Extended Falicov--Kimball Model
We consider the excitonic insulator state (often associated with electronic
ferroelectricity), which arises on the phase diagram of an extended spinless
Falicov--Kimball model (FKM) at half-filling. Within the Hartree--Fock
approach, we calculate the spectrum of low-energy collective excitations in
this state up to second order in the narrow-band hopping and/or hybridisation.
This allows to probe the mean-field stability of the excitonic insulator. The
latter is found to be unstable when the case of the pure FKM (no hybridisation
with a fully localised band) is approached. The instability is due to the
presence of another, lower-lying ground state and not to the degeneracy of the
excitonic phase in the pure FKM. The excitonic phase, however, may be
stabilised further away from the pure FKM limit. In this case, the low-energy
excitation spectrum contains new information about the properties of the
excitonic condensate (including the strongly suppressed critical temperature).Comment: 8 pages, LaTeX-Revtex, 3 PostScript figures, minor corrections. Phys.
Rev. B, in pres
Potts models with invisible states on general Bethe lattices
The number of so-called invisible states which need to be added to the
q-state Potts model to transmute its phase transition from continuous to first
order has attracted recent attention. In the q=2 case, a Bragg-Williams,
mean-field approach necessitates four such invisible states while a 3-regular,
random-graph formalism requires seventeen. In both of these cases, the
changeover from second- to first-order behaviour induced by the invisible
states is identified through the tricritical point of an equivalent
Blume-Emery-Griffiths model.
Here we investigate the generalised Potts model on a Bethe lattice with z
neighbours. We show that, in the q=2 case, r_c(z)=[4 z / 3(z-1)]
[(z-1)/(z-2)]^z invisible states are required to manifest the equivalent
Blume-Emery-Griffiths tricriticality. When z=3, the 3-regular, random-graph
result is recovered, while the infinite z limit delivers the Bragg-Williams,
mean-field result