Abstract
We consider the antiferromagnet in two dimensions by the renormalization group method. Our model is the nonlinear sigma model which is the continuum limit of the quantum antiferromagnetic Heisenberg model. Introducing fermion field (hole) in the nonlinear sigma model, we propose an effective action for the coupled spin-fermion systems. We evaluate the β-function in powers of the hole concentration δ. We show that small doping extremely reduces the correlation length ξ. We have a critical hole concentration δ c; if δ>δ c ξ becomes independent of temperature.
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