  Numerically efficient transfer matrix technique for studying statistics of
coherent adsorbates on small nanotubes has been developed. In the framework of
a realistic microscopic model fitted to the data of ab initio calculations
taken from literature sources, the ordering of potassium adsorbate on (6,0)
single-walled carbon nanotube has been studied. Special attention has been
payed to the phase transition-like abrupt changes seen in the adsorption
isotherms at low temperature. It has been found that the behavior during the
transitions conforms with the universality hypothesis of the theory of critical
phenomena and is qualitatively the same as in the one dimensional Ising model.
Quantitatively the critical behavior can be fully described by two parameters.
Their qualitative connection with the properties of interphase boundaries is
suggested but further research is needed to develop a quantitative theory.
