Rounding effects of quenched randomness on first-order phase transitions

Michael Aizenman, Jan Wehr

Research output: Contribution to journalArticle

185 Citations (Scopus)

Abstract

Frozen-in disorder in an otherwise homogeneous system, is modeled by interaction terms with random coefficients, given by independent random variables with a translation-invariant distribution. For such systems, it is proven that in d=2 dimensions there can be no first-order phase transition associated with discontinuities in the thermal average of a quantity coupled to the randomized parameter. Discontinuities which would amount to a continuous symmetry breaking, in systems which are (stochastically) invariant under the action of a continuous subgroup of O(N), are suppressed by the randomness in dimensions d≦4. Specific implications are found in the Random-Field Ising Model, for which we conclude that in d=2 dimensions at all (β, h) the Gibbs state is unique for almost all field configurations, and in the Random-Bond Potts Model where the general phenomenon is manifested in the vanishing of the latent heat at the transition point. The results are explained by the argument of Imry and Ma [1]. The proofs involve the analysis of fluctuations of free energy differences, which are shown (using martingale techniques) to be Gaussian on the suitable scale.

Original languageEnglish (US)
Pages (from-to)489-528
Number of pages40
JournalCommunications in Mathematical Physics
Volume130
Issue number3
DOIs
StatePublished - Jun 1990
Externally publishedYes

Fingerprint

First-order Phase Transition
Rounding
Randomness
Discontinuity
discontinuity
martingales
Gibbs States
Invariant Distribution
Random Coefficients
random variables
latent heat
Potts Model
Independent Random Variables
transition points
subgroups
Martingale
Symmetry Breaking
Random Field
Ising model
Ising Model

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Rounding effects of quenched randomness on first-order phase transitions. / Aizenman, Michael; Wehr, Jan.

In: Communications in Mathematical Physics, Vol. 130, No. 3, 06.1990, p. 489-528.

Research output: Contribution to journalArticle

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