Abstract
IN the literature one finds the statement that phase transitions are impossible in one-dimensional systems.1,2 “Infinities” of the parameters of the system, such as the strength of the interactions or their range, are needed3,4 in order for a phase transition to be possible. This is proved for infinite systems, which are the only ones capable of undergoing phase transitions in the mathematical sense. However, the infinities needed in the parameter values are only logarithmic in the particle number, N, and we shall show that interesting results with reasonable parameter values may still be obtained for macroscopic finite systems in one dimension. Besides the general theoretical interest of the problem, it is relevant to transitions of importance in biophysics.3,5
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