By introducing Arrhenius behaviour to the ferroparticles on the surface of the aggregated columnar structure in a diffusion model, equilibrium equations are set up. The solution of the equations shows that to keep the aggregated structures stable, a characteristic field is needed. The aggregation is enhanced by magnetic fields, yet suppressed as the temperature increases. Analysing the influence of the magnetic field on the interaction energy between the dipolar particles, we estimate the portion of the diffusing particles, and provide the agreeable ratio of the column radius over the centre-to-centre spacing between columns in a hexagonal columnar structure formed under a perpendicular magnetic field.