A simple model of Coulomb disorder and screening in graphene

We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration $N/2$ in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates two-dimensional concentration $n_0 \sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0 \sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.Comment: 2.5 pages, twice longer than previous versio

Spin-fluctuation theory beyond Gaussian approximation

A characteristic feature of the Gaussian approximation in the functional-integral approach to the spin-fluctuation theory is the jump phase transition to the paramagnetic state. We eliminate the jump and obtain a continuous second-order phase transition by taking into account high-order terms in the expansion of the free energy in powers of the fluctuating exchange field. The third-order term of the free energy renormalizes the mean field, and fourth-order term, responsible for the interaction of the fluctuations, renormalizes the spin susceptibility. The extended theory is applied to the calculation of magnetic properties of Fe-Ni Invar.Comment: 20 pages, 4 figure