We have investigated the equilibrium states of ferromagnetic single wall nanotubes by means of atomistic Monte Carlo simulations of a zig-zag lattice of Heisenberg spins on the surface of a cylinder. The main focus of our study is to determine how the competition between short-range exchange (J) and long-range dipolar (D) interactions influences the low temperature magnetic order of the nanotubes as well as the thermal-driven transitions involved. Apart from the uniform and vortex states occurring for dominant J or D, we find that helical states become stable for a range of intermediate values of g = D=J that depends on the radius and length of the nanotube. Introducing a vorticity order parameter to better characterize helical and vortex states, we find the pseudo-critical temperatures for the transitions between these states and we establish the magnetic phase diagrams of their stability regions as a function of the nanotube aspect ratio. Comparison of the energy of the states obtained by simulation with those of simpler theoretical structures that interpolate continuously between them, reveals a high degree of metastability of the helical structures that might be relevant for their reversal modes.
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