2011/04/30 by Michael Aizenman, Rafael L. Greenblatt, Joel L. Lebowitz · 29 citations
Mathematics · Physics and Astronomy · #Continuous symmetry #First order #Lattice (music) #Quantum #Quantum many-body systems #Quantum operation #Quantum phase transition #Quantum process #Quantum system #Rounding #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1063/1.3679069
published in Journal of Mathematical Physics 53(2) (American Institute of Physics) · This article presents the detailed derivation of results which were announced in Phys. Rev. Lett. 103 (2009) 197201 (arXiv:0907.2419). v3 incorporates many corrections and improvements resulting from referee comments
arxiv created 2011/11/23 · openalex publication_date 2012/02/01 · arxiv updated 2013/01/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.