Lack of self-averaging in random systems - Liability or asset?

Avishay Efrat, Moshe Schwartz

Research output: Contribution to journalArticlepeer-review

Abstract

The study of quenched random systems is facilitated by the idea that the ensemble averages describe the thermal averages for any specific realization of the couplings, provided that the system is large enough. Careful examination suggests that this idea might have a flaw, when the correlation length becomes of the order of the size of the system. We find that certain bounded quantities are not self-averaging when the correlation length becomes of the order of the size of the system. This suggests that the lack of self-averaging, expressed in terms of properly chosen signal-to-noise ratios, may serve to identify phase boundaries. This is demonstrated by using such signal-to-noise ratios to identify the boundary of the ferromagnetic phase of the random field Ising system and compare the findings with more traditional measures.

Original languageEnglish
Pages (from-to)137-142
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Volume414
DOIs
StatePublished - 15 Nov 2014

Keywords

  • Correlations
  • Ising
  • Phase-transition
  • Random
  • Self-averaging
  • Signal-to-noise

Fingerprint

Dive into the research topics of 'Lack of self-averaging in random systems - Liability or asset?'. Together they form a unique fingerprint.

Cite this