Phase transitions are not possible in one-dimensional systems due to the lack of long-range order, as established in statistical mechanics. In particular, the lattice gas model demonstrates that at low temperatures, a phase transition requires long-range order to manifest. This concept is supported by the theoretical framework outlined in "Principles of Condensed Matter Physics" by Chaikin and Lubensky. The absence of dimensionality in one-dimensional systems prevents the necessary interactions for phase transitions.
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