Phase transitions in one dimension: Are they all driven by domain walls?

2005/10/17 by N. Theodorakopoulos, Nikos Theodorakopoulos
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1016/j.physd.2005.12.016

published as Physica D 216, 185 (2006) · 9 pages, 3 figures. To appear in a special volume of Physica D (Serge Aubry 60th birthday symposium)

arxiv created 2005/10/17 · openalex publication_date 2006/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

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.

Citations

• Nonlinear Structures and Thermodynamic Instabilities in a One-Dimensional Lattice System
• Thermodynamic instabilities in one-dimensional particle lattices: A finite-size scaling approach
• General Non-Existence Theorem for Phase Transitions in One-Dimensional Systems with Short Range Interactions, and Physical Examples of Such Transitions