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

## Author(s): Aizenman, Michael; Greenblatt, Rafael L; Lebowitz, Joel L

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 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. (C) 2012 American Institute of Physics. [doi:10.1063/1.3679069] Publication Date: Feb-2012 Electronic Publication Date: 1-Feb-2012 Citation: Aizenman, Michael, Greenblatt, Rafael L, Lebowitz, Joel L. (2012). Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems. JOURNAL OF MATHEMATICAL PHYSICS, 53 (10.1063/1.3679069 DOI: doi:10.1063/1.3679069 ISSN: 0022-2488 Type of Material: Journal Article Journal/Proceeding Title: JOURNAL OF MATHEMATICAL PHYSICS Version: Author's manuscript