Rounding of First Order Transitions in Low-Dimensional Quantum Systems with Quenched Disorder

2009/07/31 by Rafael L. Greenblatt, Michael Aizenman, Joel L. Lebowitz · 2 citations
Physics and Astronomy · Mathematics · #cond-mat.stat-mech #cond-mat.dis-nn #math-ph #math.MP

paper · pdf · doi:10.1103/physrevlett.103.197201

published as Phys. Rev. Lett. 103 (2009) 197201 · Four pages, RevTex. Minor corrections

arxiv created 2009/11/03 · arxiv updated 2010/10/26

Abstract

We prove that the addition of an arbitrarily small random perturbation of a suitable type to a quantum spin system rounds a first order phase transition in the conjugate order parameter in d <= 2 dimensions, or in systems with continuous symmetry in d <= 4. This establishes rigorously for quantum systems the existence of the Imry-Ma phenomenon, which for classical systems was proven by Aizenman and Wehr.

Cited by

• Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems
• Infinite Stability in Disordered Systems