General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
The authors undertake the critique of a famous general statement, namely there cannot be phase transitions in one-dimensional systems with short range interactions. To carry out this program, they proceed along two complementary directions. First, they review the existing results about nonexistence of phase transitions in short-ranged one-dimensional systems. The authors note that the well-known argument by Landau about domain walls is heuristic and relies on approximate calculations; they also comment briefly on this. Next, the authors discuss several one-dimensional models proposed in the past which exhibit true thermodynamic phase transitions. Having thus established clearly the existence of phase transitions in one-dimensional systems with short range interactions, they move their second contribution, introducing rigorously a very general theorem on the impossibility of phase transitions in such models. The authors also show how models not fulfilling one of the hypothesis exist which do have phase transitions and comment on the ways to violate those hypotheses.
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