  The statement that any phase transition is related to the appearance or
disappearance of long-range spatial correlations precludes a finite transition
temperature in one-dimensional (1D) systems. In this paper we demonstrate that
the 1D Ising model with short-range exchange interactions exhibits a
second-order phase transition at a finite temperature relying on the proper
choice of the order parameter. To accomplish this, we combined analytical
calculations and high-precision entropic sampling simulations and chose a
slightly different order parameter, namely the module of the magnetization.
Notably, we detected a phase transition with a corresponding critical
temperature around 15 K, which is in excellent agreement with experimental
results. Our study indicates that an inappropriate choice of the order
parameter may mask phase transitions in one-dimensional systems.
