Order-Disorder Transition in the Two-Dimensional Antiferromagnet

Abstract

Order-disorder transition of the doped antiferromagnet in two-dimensional space is considered, based on the quantum mechanical nonlinear sigma model. Introducing fermion fields in the nonlinear sigma model, we evaluate the β-function in powers of the hole concentration δ. We show that doped holes greatly reduce the correlation length ξ and lead to a breakdown of the antiferromagnetic long-range order at T=0 if δ>δ_c, where δ_c is a critical hole concentration. We obtain three distinct regions characterized by the behavior of the correlation length as a function of temperature.