Condensed Matter Physics, 2014, vol. 17, No. 3, p. 33601:1-11

Title: Stability of the Griffiths phase in a 2D Potts model with correlated disorder
  C. Chatelain (Groupe de Physique Statistique, Département P2M, Institut Jean Lamour, CNRS (UMR 7198), Université de Lorraine, France)

A Griffiths phase has recently been observed by Monte Carlo simulations in the 2D q-state Potts model with strongly correlated quenched random couplings. In particular, the magnetic susceptibility was shown to diverge algebraically with the lattice size in a broad range of temperatures. However, only relatively small lattice sizes could be considered, so one can wonder whether this Griffiths phase will not shrink and collapse into a single point, the critical point, as the lattice size is increased to much larger values. In this paper, the 2D eight-state Potts model is numerically studied for four different disorder correlations. It is shown that the Griffiths phase cannot be explained as a simple spreading of local transition temperatures caused by disorder fluctuations. As a consequence, the vanishing of the latter in the thermodynamic limit does not necessarily imply the collapse of the Griffiths phase into a single point. By contrast, the width of the Griffiths phase is controlled by the disorder strength. However, for disorder correlations decaying slower than 1/r, no cross-over to a more usual critical behavior could be observed as this strength is tuned to weaker values.

Key words: critical phenomena, random systems, Griffiths phase, Potts model, Monte Carlo simulations
PACS: 64.60.De, 05.50.+q, 05.70.Jk, 05.10.Ln

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