Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Michael Aizenman, Rafael L. Greenblatt, Joel L. Lebowitz

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19 Scopus citations

Abstract

We prove that for quantum lattice systems in d ≤ 2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T = 0. For systems with continuous symmetry the statement extends up to d ≤ 4 dimensions. This establishes for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr. The extension of the proof to quantum systems is achieved by carrying out the analysis at the level of thermodynamic quantities rather than equilibrium states.

Original languageEnglish (US)
Article number023301
JournalJournal of Mathematical Physics
Volume53
Issue number2
DOIs
StatePublished - Feb 2 2012

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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