Singular self-energy for itinerant electrons in a dilute Ising spin bath

We consider itinerant spinless electrons moving as defects in a dilute two-dimensional Ising spin system, leading to an effective interaction mediated by spin fluctuations. Coupled self-consistent equations are analyzed after expressing the spin and fermion operators in terms of Grassmann variables. The effective mass, density of states, and specific heat are evaluated. We found that at low temperature and low electron density the effective mass is reduced, whereas in the critical region it sharply diverges. At higher temperature, the fermions behave like a Fermi liquid with a small enhanced mass.