Spin correlation in fermion-doped nonlinear sigma model

We study the low-temperature behavior of a quantum nonlinear σ model (NLσM) in two space dimensions. This model is considered to describe the long-wavelength limit of the two-dimensional Heisenberg antiferromagnet. The correlation function is calculated in a 1/n expansion. We find a crossover between classical and quantum regimes as the temperature is reduced. Introducing fermion fields in NLσM, we propose a model of the doped antiferromagnet. It is shown that doped holes extremely reduce the correlation length ξ. We have a critical hole concentration δc; if δ>δc, ξ becomes independent of temperature.