  A novel mean-field approximation for quasi-one-dimensional (Q1D) quantum
magnets is formulated. Our new mean-field approach is based on the Bethe-type
effective-field theory, where thermal and quantum fluctuations between the
nearest-neighbor chains as well as those in each chain are taken into account
exactly. The self-consistent equation for the critical temperature contains the
boundary-field magnetic susceptibilities of a multichain cluster, which can be
evaluated accurately by some analytic or numerical methods, such as the
powerful quantum Monte Carlo method. We show that the accuracy of the critical
temperature of Q1D magnets as a function of the strength of interchain coupling
is significantly improved, compared with the conventional chain mean-field
theory. It is also demonstrated that our new approximation can predict
nontrivial dependence of critical temperature on the sign (i.e., ferromagnetic
or antiferromagnetic) of interchain coupling as well as on the impurity
concentration in randomly diluted Q1D Heisenberg antiferromagnets.
