Weak ferromagnetism with the Kondo screening effect in the Kondo lattice systems

We carefully consider the interplay between ferromagnetism and the Kondo screening effect in the conventional Kondo lattice systems at finite temperatures. Within an effective mean-field theory for small conduction electron densities, a complete phase diagram has been determined. In the ferromagnetic ordered phase, there is a characteristic temperature scale to indicate the presence of the Kondo screening effect. We further find two distinct ferromagnetic long-range ordered phases coexisting with the Kondo screening effect: spin fully polarized and partially polarized states. A continuous phase transition exists to separate the partially polarized ferromagnetic ordered phase from the paramagnetic heavy Fermi liquid phase. These results may be used to explain the weak ferromagnetism observed recently in the Kondo lattice materials.Comment: 6 pages, 6 figures; published versio

Tensor stability in Born-Infeld determinantal gravity

We consider the transverse-traceless tensor perturbation of a spatial flat homogeneous and isotropic spacetime in Born-Infeld determinantal gravity, and investigate the evolution of the tensor mode for two solutions in the early universe. For the first solution where the initial singularity is replaced by a regular geometric de Sitter inflation of infinite duration, the evolution of the tensor mode is stable for the parameter spaces $\alpha<-1$, $\omega\geq-1/3$ and $\alpha=-1$, $\omega>0$. For the second solution where the initial singularity is replaced by a primordial brusque bounce, which suffers a sudden singularity at the bouncing point, the evolution of the tensor mode is stable for all regions of the parameter space. Our calculation suggests that the tensor evolution can hold stability in large parameter spaces, which is a remarkable property of Born-Infeld determinantal gravity. We also constrain the theoretical parameter $|\lambda|\geq 10^{-38} \text{m}^{-2}$ by resorting to the current bound on the speed of the gravitational waves.Comment: 14 pages, added a general discussion on the tensor stability in Sec. 3, and added Sec. 5 on the parameter constraint, published versio

Coupling of pion condensate, chiral condensate and Polyakov loop in an extended NJL model

The Nambu Jona-Lasinio model with a Polyakov loop is extended to finite isospin chemical potential case, which is characterized by simultaneous coupling of pion condensate, chiral condensate and Polyakov loop. The pion condensate, chiral condensate and the Polyakov loop as functions of temperature and isospin chemical potential are investigated by minimizing the thermodynamic potential of the system. The resulting $(T,\mu_I)$ phase diagram is studied with emphasis on the critical point and Polyakov loop dynamics. The tricritical point for the pion superfluidity phase transition is confirmed and the phase transition for isospin symmetry restoration in high isospin chemical potential region perfectly coincides with the crossover phase transition for Polyakov loop. These results are in agreement with the Lattice QCD data.Comment: 15pages, 8 figure