  The effect of the anisotropy in the exchange interaction on the critical
temperature and the order parameter of the anisotropic Heisenberg model on a
core-shell structured nanotube geometry has been investigated. As a
formulation, effective field theory with the differential operator technique
and decoupling approximation within the 4-spin cluster (EFT-4) has been used.
The variation of the critical temperature with the anisotropy in the exchange
interaction has been obtained. Besides, suitability of the effective field
theory in small clusters as a formulation for the Heisenberg nanotube has been
discussed and it is concluded that minimum size of the cluster is 4-spin
cluster, which can give the correct critical description of the system.
