Condensed Matter Physics, 2014, vol. 17, No. 3, p. 33601:111
DOI:10.5488/CMP.17.33601
Title:
Stability of the Griffiths phase in a 2D Potts model with correlated disorder
Author(s):

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 qstate 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 eightstate 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 crossover 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
