Ground state and thermal properties of a lattice gas on a cylindrical   surface
  Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with an approximate model of adsorption on lattice sites situated on a cylindrical surface. Using this model, the ground state energies of alternative lattice structures are calculated, assuming Lennard-Jones pair interactions between the particles. The resulting energy and equilibrium structure are nonanalytic functions of radius (R) because of commensuration effects associated with the cylindrical geometry.   Specifically, as R varies, structural transitions occur between configurations differing in the "ring number", defined as the number of atoms located at a common value of the longitudinal coordinate (z). The thermodynamic behavior of this system is evaluated at finite temperatures, using a Hamiltonian with nearest-neighbor interactions. The resulting specific heat bears a qualitative resemblance to that of the one-dimensional Ising model. 
M. Mercedes Calbi, Silvina M. Gatica, Mary J. Bojan, and Milton W.   Cole