Phase transitions in one dimension and less

2002/02/08 by Paul Fendley, Oleg Tchernyshyov
Physics and Astronomy · #Quantum many-body systems #Statistical Mechanics and Entropy #Theoretical and Computational Physics #cond-mat.stat-mech #cond-mat.str-el #hep-th

paper · pdf · doi:10.1016/s0550-3213(02)00481-9

published as Nucl.Phys. B639 (2002) 411-428 · 16 pages, 1 figure

arxiv created 2002/02/08 · openalex publication_date 2002/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Phase transitions can occur in one-dimensional classical statistical mechanics at non-zero temperature when the number of components N of the spin is infinite. We show how to solve such magnets in one dimension for any N, and how the phase transition develops at N = infinity. We discuss SU(N) and Sp(N) magnets, where the transition is second-order. In the new high-temperature phase, the correlation length is zero. We also show that for the SU(N) magnet on exactly three sites with periodic boundary conditions, the transition becomes first order.

Citations

• Liquid–gas and other unusual thermal phase transitions in some large-N magnets

Related

• Liquid–gas and other unusual thermal phase transitions in some large-N magnets
• Unveiling phase transitions in 1D systems with short-range interactions
• Finding and classifying an infinite number of cases of the marginal phase transition in one-dimensional Ising models
• No or diffuse phase transition with temperature in one-dimensional Ising model?
• An example of one-dimensional phase transition