Percolation and Schramm–Loewner evolution in the 2D random-field Ising model

J. D. Stevenson, Martin Weigel

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The presence of random fields is well known to destroy ferromagnetic order in Ising systems in two dimensions. When the system is placed in a sufficiently strong external field, however, the size of clusters of like spins diverges. There is evidence that this percolation transition is in the universality class of standard site percolation. It has been claimed that, for small disorder, a similar percolation phenomenon also occurs in zero external field. Using exact algorithms, we study ground states of large samples and find little evidence for a transition at zero external field. Nevertheless, for sufficiently small random-field strengths, there is an extended region of the phase diagram, where finite samples are indistinguishable from a critical percolating system. In this regime we examine ground-state domain walls, finding strong evidence that they are conformally invariant and satisfy Schramm–Loewner evolution (SLEκ) with parameter κ=6. These results add support to the hope that at least some aspects of systems with quenched disorder might be ultimately studied with the techniques of SLE and conformal field theory.
Original languageEnglish
Pages (from-to)1879–1882
JournalComputer Physics Communications
Volume182
Issue number9
DOIs
Publication statusPublished - 4 Dec 2010

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Ising model
Ground state
Domain walls
disorders
Phase diagrams
ground state
domain wall
field strength
phase diagrams

Bibliographical note

The full text is not available on the repository.

Keywords

  • Schramm (stochastic)
  • Loewner evolution
  • Percolation
  • Random-field Ising model

Cite this

Percolation and Schramm–Loewner evolution in the 2D random-field Ising model. / Stevenson, J. D.; Weigel, Martin.

In: Computer Physics Communications, Vol. 182, No. 9, 04.12.2010, p. 1879–1882.

Research output: Contribution to journalArticle

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