Phase transitions are generally not possible in one-dimensional systems due to the lack of long-range order, which is essential for such transitions to occur. In one dimension, thermal fluctuations dominate, preventing the establishment of the necessary order. For a lattice gas at low temperatures, long-range order is required to achieve a phase transition, as local interactions alone cannot stabilize the system. The discussion highlights uncertainty about the specifics, with references to established literature like Chaikin and Lubensky for further clarification. Overall, the complexity of one-dimensional systems limits their ability to undergo phase transitions.
