Calculation of Neel temperature forS=1/2Heisenberg quasi-one-dimensional antiferromagnets

Isotropic $S=1/2\mathrm{}$ quasi-one-dimensional antiferromagnets are considered within the bosonization method. The ${1/z}_{\perp }$ corrections to the interchain mean-field theory (where $z_{\perp }$ is the number of nearest neighbors in transverse to chain directions) are obtained for the ground-state sublattice magnetization $S_0$ and Neel temperature $T_N.$ The corrections to $T_N$ make up about 25% of mean-field value, while those to $S_0$ are small enough (especially in the three-dimensional case). The fluctuation corrections obtained improve considerably the agreement with the experimental data for magnetic-chain compounds ${\mathrm{KCuF}}_3,$ ${\mathrm{Sr}}_2{\mathrm{CuO}}_3,$ and ${\mathrm{Ca}}_2{\mathrm{CuO}}_3.$