Instability of the paramagnetic state towards incommensurate magnetic order in the 2-d Hubbard model

We determine the instability line separating the paramagnetic phase in the phase diagram of the 2-d Hubbard Model from a phase with incommensurate magnetic order. A mean-field approximation of the Kotliar-Ruckenstein slave boson representation is used to calculate the wave-vector dependent magnetic susceptibility. For largeU/t the instability occurs at a densityn0.37, and a wave-vector close toq=(0,). The dependence ofq onU andn is also given.     

On the spectrum of the sum of generators for a finitely generated group

Let Γ be a finitely generated group. In the group algebra ℂ[Γ], form the averageh of a finite setS of generators of Γ. Given a unitary representation π of Γ, we relate spectral properties of the operator π(h) to properties of Γ and π. For the universal representationπ _un of Γ, we prove in particular the following results. First, the spectrum Sp(π _un (h)) contains the complex numberz of modulus one iff Sp(π _un (h)) is invariant under multiplication byz, iff there exists a character such that η(S)={z}. Second, forS ⁻¹=S, the group Γ has Kazhdan’s property (T) if and only if 1 is isolated in Sp(π _un (h)); in this case, the distance between 1 and other points of the spectrum gives a lower bound on the Kazhdan constants. Numerous examples illustrate the results.     

Electron diffraction studies of the molecular structures of iron(II) chloride and iron(II) bromide. Evidence on the structure of dimeric species Fe2Br4

An expression for the extreme values of mean-square amplitudes of vibrations in polyatomic molecules has been derived which permits estimation of the mean-square amplitude without solving the vibrational problem. This expression can be improved for the stretching and scissoring modes when the assignment of frequencies is known. In turn, the corresponding vibrational frequency may be estimated from the experimental value of the mean-square amplitude. The mean-square amplitudes of the butadiene-1,3 molecule are considered as an example.