On spin systems with quenched randomness: Classical and quantum

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

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 15, 2902-2906

Abstract: The rounding of first-order phase transitions by quenched randomness is stated in a form which is applicable to both classical and quantum systems: The free energy, as well as the ground state energy, of a spin system on a d-dimensional lattice is continuously differentiable with respect to any parameter in the Hamiltonian to which some randomness has been added when d≤2. This implies absence of jumps in the associated order parameter, e.g., the magnetization in the case of a random magnetic field. A similar result applies in cases of continuous symmetry breaking for d≤4. Some questions concerning the behavior of related order parameters in such random systems are discussed.

Keywords: Quenched disorder; Lattice spin systems (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:15:p:2902-2906

DOI: 10.1016/j.physa.2009.12.066

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