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On spin systems with quenched randomness: Classical and quantum

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

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.

Suggested Citation

  • Greenblatt, Rafael L. & Aizenman, Michael & Lebowitz, Joel L., 2010. "On spin systems with quenched randomness: Classical and quantum," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(15), pages 2902-2906.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:15:p:2902-2906
    DOI: 10.1016/j.physa.2009.12.066
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    References listed on IDEAS

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    1. Malakis, A. & Berker, A. Nihat & Hadjiagapiou, I.A. & Fytas, N.G. & Papakonstantinou, T., 2010. "Uncovering the secrets of the 2D random-bond Blume–Capel model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(15), pages 2930-2933.
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      Keywords

      Quenched disorder; Lattice spin systems;

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