On spin systems with quenched randomness: Classical and quantum

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

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2902-2906
Number of pages5
JournalPhysica A: Statistical Mechanics and its Applications
Issue number15
StatePublished - Aug 1 2010

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics


  • Lattice spin systems
  • Quenched disorder


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