The phase structure and IR properties of the higher-derivative quantum
gravity (QG) with scalar matter in 4 - epsilon dimensions are investi
gated. The appearance of a few fixed points of the renormalization gro
up (one of them is an infrared stable fixed point) is numerically show
n. The new fixed points in 3 dimensions are associated with QG. The na
ture of phase transitions at nonzero temperature is discussed, and the
improved effective potential is calculated.