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Temporal disorder in up-down symmetric systems

Ricardo Martínez-García1, Federico Vazquez2, Cristóbal López1, and Miguel A. Muñoz3

  • 1IFISC, Instituto de Física Interdisciplinar y Sistemas Complejos (CSIC-UIB), E-07122 Palma de Mallorca, Spain
  • 2Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, Germany
  • 3Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada, Spain

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Phys. Rev. E 85, 051125 – Published 16 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.051125

Abstract

The effect of temporal disorder on systems with up-down Z2 symmetry is studied. In particular, we analyze two well-known families of phase transitions—the Ising and the generalized voter universality classes—and scrutinize the consequences of placing them under fluctuating global conditions. We observe that variability of the control parameter induces in both classes “temporal Griffiths phases” (TGPs). These recently uncovered phases are analogous to standard Griffiths phases appearing in systems with quenched spatial disorder, but where the roles of space and time are exchanged. TGPs are characterized by broad regions in parameter space in which (i) mean first-passage times scale algebraically with system size, and (ii) the system response (e.g., susceptibility) diverges. Our results confirm that TGPs are quite robust and ubiquitous in the presence of temporal disorder. Possible applications of our results to examples in ecology are discussed.

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Phys. Rev. E 85, 051125– Published 16 May, 2012
  • Received 24 February 2012

©2012 American Physical Society

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