TOPICAL REVIEW: Rare region effects at classical, quantum and nonequilibrium phase transitions

@article{Vojta2006TOPICALRR,
  title={TOPICAL REVIEW: Rare region effects at classical, quantum and nonequilibrium phase transitions},
  author={Thomas Vojta},
  journal={Journal of Physics A},
  year={2006}
}
  • T. Vojta
  • Published 13 February 2006
  • Physics
  • Journal of Physics A
Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions and in systems with correlated disorder. In some… 

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References

SHOWING 1-10 OF 284 REFERENCES

Modern Theory of Critical Phenomena

An important contributor to our current understanding of critical phenomena, Ma introduces the beginner--especially the graduate student with no previous knowledge of the subject-to fundamental

Phase Transitions and Critical Phenomena, volume 8, ed C

  • Domb and J L Lebowitz (New York: Academic)
  • 1983

Rare region effects at classical, quantum, and nonequilibrium phase transitions

  • Phys. Rev. Lett
  • 1985

Finite-size scaling

Preface. Acknowledgements. 1. Theory of Finite-Size Scaling. Contributors: M.N. Barber, K. Binder, E. Brezin, E. Eisenriegler, M.E. Fisher, Y.Y. Goldschmidt, H. Guo, D. Jasnow, M. Nauenberg, V.

Nanoscale Phase Separation and Colossal Magnetoresistance

Non-Fermi-liquid behavior in d - and f -electron metals

A relatively new class of materials has been found in which the basic assumption of Landau Fermi-liquid theory—that at low energies the electrons in a metal should behave essentially as a collection

Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation

A theory of equations of state and phase transitions is developed that describes the condensed as well as the gas phases and the transition regions. The thermodynamic properties of an infinite sample

Effect of random defects on the critical behaviour of Ising models

A cumulant expansion is used to calculate the transition temperature of Ising models with random-bond defects. For a concentration, x, of missing interactions in the simple-square Ising model the
...