Magnetic order and spin fluctuations in low-dimensional insulating systems

The current theoretical and experimental situations are reviewed for low-dimensional insulating systems with a low magnetic transition temperature $T_M$ and pronounced short-range magnetic order above this temperature. Both the standard and self-consistent spin-wave theories are shown to be insufficient to quantitatively describe the experimental data on these systems. Field-theoretical approaches taking into account the contribution of the spin-fluctuation excitations (neglected in the spin-wave theories) to the thermodynamic properties of ferro- and antiferromagnets are discussed.