ORDER-DISORDER TRANSITION IN THE 2-DIMENSIONAL ANTIFERROMAGNET

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 beta-function in powers of the hole concentration-delta. We show that doped holes greatly reduce the correlation length-xi and lead to a breakdown of the antiferromagnetic long-range order at T = 0 if delta > delta-c, where delta-c is a critical hole concentration. We obtain three distinct regions characterized by the behavior of the correlation length as a function of temperature.