Bounded Fluctuations and Translation Symmetry Breaking in One-Dimensional Particle Systems

Simple item page
dc.creatorAizenman, M.
dc.creatorGoldstein, S.
dc.creatorLebowitz, J. L.
dc.date2000-07-14
dc.date2000-11-03
dc.date.accessioned2026-07-07T04:27:54Z
dc.date.available2026-07-07T04:27:54Z
dc.descriptionWe present general results for one-dimensional systems of point charges (signed point measures) on the line with a translation invariant distribution $μ$ for which the variance of the total charge in an interval is uniformly bounded (instead of increasing with the interval length). When the charges are restricted to multiples of a common unit, and their average charge density does not vanish, then the boundedness of the variance implies translation-symmetry breaking --- in the sense that there exists a function of the charge configuration that is nontrivially periodic under translations --- and hence that $μ$ is not ``mixing.'' Analogous results are formulated also for one dimensional lattice systems under some constraints on the values of the charges at the lattice sites and their averages. The general results apply to one-dimensional Coulomb systems, and to certain spin chains, putting on common grounds different instances of symmetry breaking encountered there.
dc.descriptionLaTex document, 24 pp
dc.identifierhttps://arxiv.org/abs/math-ph/0007022
dc.identifierhttp://arxiv.org/abs/math-ph/0007022
dc.identifierJ. Stat. Phys., v. 103, 601 (2001).
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56588
dc.subjectMathematical Physics
dc.subjectStrongly Correlated Electrons
dc.subjectProbability
dc.subject82B99; 60D05
dc.titleBounded Fluctuations and Translation Symmetry Breaking in One-Dimensional Particle Systems
dc.typetext

Files

Collections

arXiv