Rounding Effects in Systems with Static Disorder

  • Jan Wehr
Conference paper

Abstract

Condensed matter physics often has to consider systems with static disorder [6], [7], i.e. with impurities, dislocations, substitutions etc. which vary from sample to sample (thus introducing disorder) but which do not exhibit thermal fluctuations on relevant time scales (hence the word static). To account for such disorder mathematically one often uses lattice spin systems with random parameters in the interaction (e.g. random magnetic fields or random coupling constants). For each fixed realization of these parameters one then obtains a spin system in which the usual quantities of physical interest — magnetization, free energy etc. — can be calculated. Random parameters of this type are often called quenched, to stress the fact that they remain constant during the calculation of spin averages — corresponding to the static nature of the disorder in the modelled physical system.

Keywords

Entropy 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aizenman, M., Wehr, J.: Rounding of First-Order Phase Transitions in Systems with Quenched Disorder. Phys.Rev.Lett. 62, 2503 (1989)MathSciNetCrossRefADSGoogle Scholar
  2. 2.
    Aizenman, M., Wehr, J.: Rounding Effects of Quenched Randomness on First-Order Phase Transitions. Comm.Math.Phys. 130, 489 (1990)MathSciNetCrossRefMATHADSGoogle Scholar
  3. 3.
    Bricmont, J., Kupiainen, A.: Lower critical Dimension for the Random-Field Ising Model. Phys.Rev.Lett. 59, 1829 (1987);MathSciNetCrossRefADSGoogle Scholar
  4. 3a.
    Bricmont, J., Kupiainen, A.: Phase Transition in the Random-Field Ising Model. Comm.Math.Phys. 116, 539 (1988)MathSciNetCrossRefADSGoogle Scholar
  5. 4.
    Imbrie, J.Z.: Lower Critical Dimension of the Random-Field Ising Model. Phys.Rev.Lett. 53, 1747 (1984);CrossRefADSGoogle Scholar
  6. 4a.
    Imbrie, J.Z.: The Ground State of the Three-Dimensional Random-Field Ising Model. Comm.Math.Phys. 98, 145 (1985)MathSciNetCrossRefMATHADSGoogle Scholar
  7. 5.
    Kotecky, R., Shlosman, R.: First-Order Phase Transitions in Large Entropy Lattice Models. Comm.Math.Phys. 83, 493 (1982)MathSciNetCrossRefADSGoogle Scholar
  8. 6.
    Balian, R., Manyard, R., Toulouse, G. (eds.): Ill-Condensed Matter. North-Holland, Amsterdam (1979)Google Scholar
  9. 7.
    Osterwalder, K., Stora, R. (eds.): Critical Phenomena, Random Systems, Gauge Theories. Vol.11. North-Holland, Amsterdam (1986)Google Scholar
  10. 8.
    Imry, Y, Ma, S.-K: Random-Field Instability of the Ordered State of Continuous Symmetry. Phys.Rev.Lett. 35, 1399 (1975)CrossRefADSGoogle Scholar
  11. 9.
    Wehr, J.: Effects of Static Disorder in Statistical Mechanics: Absence of a Phase Transition in the Two-Dimensional Random-Field Ising Model. In: Morrow, G.J., Yang, W.S. (eds.): Probability Models in Mathematical Physics. World Scientific (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Jan Wehr
    • 1
  1. 1.Institute for Advanced StudyPrincetonUSA

Personalised recommendations