  We study the two-dimensional periodic Anderson model at half-filling using
quantum Monte Carlo (QMC) techniques. The ground state undergoes a magnetic
order-disorder transition as a function of the effective exchange coupling
between the conduction and localized bands. Low-lying spin and charge
excitations are determined using the maximum entropy method to analytically
continue the QMC data. At finite temperature we find a competition between the
Kondo effect and antiferromagnetic order which develops in the localized band
through Ruderman-Kittel-Kasuya-Yosida interactions.
