Phase transitions in one dimension: are they all driven by domain walls?
arXiv:cond-mat/0510437 · doi:10.1016/j.physd.2005.12.016
Abstract
Two known distinct examples of one-dimensional systems which are known to exhibit a phase transition are critically examined: (A) a lattice model with harmonic nearest-neighbor elastic interactions and an on-site Morse potential, and (B) the ferromagnetic, spin 1/2 Ising model with long-range pair interactions varying as the inverse square of the distance between pairs. In both cases it can be shown that the domain wall configurations become entropically stable at, or very near, the critical temperature. This might provide a "positive" criterion for the occurrence of a phase transition in one-dimensional systems.
9 pages, 3 figures. To appear in a special volume of Physica D (Serge Aubry 60th birthday symposium)
References in corpus (3)
- General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
- Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system
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- Exact solution of a classical short-range spin model with a phase transition in one dimension: the Potts model with invisible states
- Classical phase transitions in a one-dimensional short-range spin model induced by entropy depletion or complex fields
- Differences in the scaling laws of canonical and microcanonical coarsening dynamics for long-range interacting systems