### 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 language | English (US) |
---|---|

Pages (from-to) | 489-528 |

Number of pages | 40 |

Journal | Communications in Mathematical Physics |

Volume | 130 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

*130*(3), 489-528. https://doi.org/10.1007/BF02096933

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 130, no. 3, pp. 489-528. https://doi.org/10.1007/BF02096933

}

TY - JOUR

T1 - Rounding effects of quenched randomness on first-order phase transitions

AU - Aizenman, Michael

AU - Wehr, Jan

PY - 1990/6

Y1 - 1990/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=11744381258&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=11744381258&partnerID=8YFLogxK

U2 - 10.1007/BF02096933

DO - 10.1007/BF02096933

M3 - Article

AN - SCOPUS:11744381258

VL - 130

SP - 489

EP - 528

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -