We have analyzed the modulated phase ot' an Ising model with competing interactions in an et'fort to increase the understanding of the spatially modulated phases t'ound in many physical systems. The analysis has three stages. First, the mean-field phase diagram is calculated numerically. A large, possibly infinite, number of phases where the periodicity ot' the ordered structure is cornrnensurate with the lattice is f'ound. The resulting periodicity-versus- temperature curve thus probably has an inf'inity of'steps; i.e. , it exhibits "the devil's staircase" behavior. Then the mean-field theory is analyzed analytically, and it is shown that the stability of' the commensurate phases can be understood within a domain-wall or "soliton" theory. The solitons from a regular lattice near the transitions to the commensurate phases. The elementary excitations in the soliton lattice are the phasons. Third, the effects of' temperature-induced fluctuations, ignored in the mean-field theory, are estimated by calculating the entropy contribution to the free energy f'rom the phasons. It is found that the stability ranges of the commensurate phases are reduced, but the staircase survives at finite temperatures.
On the basis of our calcu- lations a phase diagram is constructed.