Diagrammatic perturbation theory and the pseudogap

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical molecular fields. We consider two types of such fields, a vector molecular field that couples to the quasiparticle spin-density and a scalar field coupled to the quasiparticle number density. The model describes quasiparticles coupled to spin or charge fluctuations, and is solved by a Monte Carlo sampling of the molecular field distributions. The nonperturbative solution is compared to various approximations based on diagrammatic perturbation theory. When the molecular field correlations are sufficiently weak, the diagrammatic calculations capture the qualitative aspects of the quasiparticle spectrum. For a range of model parameters near the magnetic boundary, we find that the quasiparticle spectrum is qualitatively different from that of a Fermi liquid, in that it shows a double peak structure, and that the diagrammatic approximations we consider fail to reproduce, even qualitatively, the nonperturbative results of the Monte Carlo calculations. This suggests that the magnetic pseudogap induced by a coupling to antiferromagnetic spin-fluctuations and the spin-splitting of the quasiparticle peak induced by a coupling to ferromagnetic spin-fluctuations lie beyond diagrammatic perturbation theory. While a pseudogap opens when quasi-