Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 01, 2012
- Source ID
- 10.1063/1.3679069
Entities
People
- Joel Lebowitz
- Michael Aizenman
- Rafael L. Greenblatt
Organizations
- Air Force Office of Scientific Research
- National Science Foundation
- Princeton University
- Rutgers University
- Università degli Studi Roma Tre