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Static and dynamical properties of weakly coupled antiferromagnetic spin chains are treated using a mean-field approximation for the interchain coupling and exact results for the resulting effective one-dimensional problem.Results for staggered magnetization, Néel temperature and spin wave excitations are in agreement with experiments on KCuF 3 . The existence of a narrow longitudinal mode is predicted. The results are in agreement with general scaling arguments, contrary to spin wave theory. 75.10Jm, 75.30Cr, 75.30Ds, 75.50Ee Typeset using REVT E X

We calculate the spin sti ness s for the frustrated spin-1 2 Heisenberg antiferromagnet on a square lattice by exact diagonalizations on nite clusters of up to 36 sites followed by extrapolations to the thermodynamic limit. For the non-frustrated case, we nd that s = (0:183 0:003)J1, in excellent agreement with the best results obtained by other means. Turning on frustration, the extrapolated sti ness vanishes for 0:4 < J2=J1 < 0:6. In this intermediate region, the nite-size scaling works poorly { an additional sign that their is neither N eel nor collinear magnetic order. Using a hydrodynamic relation, and previous results for the transverse susceptibility, we also estimate the spin-wave velocity in the N eel-ordered region.The question of the existence of long{range magnetic order (LRMO) in systems with frustrated interactions and strong (quantum or thermal) uctuations is often di cult to decide. The traditional way of answering this question is by calculating magnetic order parameters. An alternative way is to consider the spin sti ness s , which is non-zero in a LRMO state. The sti ness has the advantage of being unbiased with respect to the order parameter, and constitutes, together with the spin-wave velocity, the fundamental parameter that determines the low-energy dynamics of magnetic systems 1]. It is therefore of importance to nd accurate values for s .The spin sti ness measures the energy cost to introduce a twist of the direction of spin between every pair of neighboring rows,(1) where E 0 ( ) is the ground-state energy as a function of the imposed twist, and N is the number of sites. In the thermodynamic limit, a positive value of s means that LRMO persists in the system, while a zero value reveals that there is no LRMO, as is the case in a spinliquid. When looking at a nite system, things are more complicated. Here the sti ness is only zero at distinct points, and is positive or negative on the intervals in between. A negative value says that the system is unstable to a change in the boundary conditions, suggesting that the true ground state of the model in the thermodynamic limit is incommensurate with the structure of the nite cluster being used. A positive value reveals a stable ground state, and can sometimes be used with nite-size scaling to extract the behavior of the sti ness in the thermodynamic limit. This is in particular the case in the N eel and collinear regions.The spin sti ness for the unfrustrated spin-1 2 Heisenberg model on a 2D square lattice has been calculated directly by series expansion 2], s = (0:18 0:01)J 1 , and by second-order spin-wave theory (SSWT) 3], s = (0:181 0:001)J 1 . Furthermore, the spin-wave velocity c and the transverse susceptibility ? have also been calculated in SSWT, and since the ensemble of values ful ll the hydrodynamic relation 1] s = c 2 ? to a good approximation, there is strong evidence for the accuracy of the SSWT values 3]. However, a previous attempt to extract the value of s from exact diagonalizations (ED) yielded s = 0:125J 1 4], which is far...