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First-principles density functional calculations for graphene and defectedgraphene are used to examine when the quasi-2D electrons near the Fermi energyin graphene could be represented by massless fermions obeying a Dirac-Weyl (DW)equation. The DW model is found to be inapplicable to defected graphenecontaining even $\sim$3% vacancies or N substitution. However, the DW modelholds in the presence of weakly adsorbed molecular layers. The possibility ofspin-polarized phases (SPP) of DW-massless fermions in pure graphene isconsidered. The exchange energy is evaluated from the analyticpair-distribution functions as well as in $k$-space. The kinetic energyenhancement of the sipn-polarized phase nearly cancels the exchangeenhancement, and the correlation energy plays a dominant residual role. Thecorrelation energies are estimated via a model four-component 2D electron fluidwhose Coulomb coupling matches that of graphene. While SPPs appear withexchange only, the inclusion of correlations suppresses them in ideal graphene.Comment: ~7 pages, 6 figure

Ground state of clean and defective graphene: Coulomb interactions, pair-distribution functions, and spin-polarized phases of massless Dirac fermions