1998/04/29 by Ferenc Iglói, F. Igloi, Heiko Rieger +1 · 1 citation
Mathematics · Physics and Astronomy · #Anomalous diffusion #Diffusion #Ising model #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum mechanics #Random field #Random walk #Spin (aerodynamics) #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.58.4238
published as Phys. Rev. E 58, 4238 (1998) · 4 pages RevTeX, 1 eps-figures included
arxiv created 1998/04/29 · openalex publication_date 1998/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Using exact expressions for the persistence probability and for the leading eigenvalue of the Fokker-Planck operator of a random walk in a random environment, we establish a fundamental relation between the statistical properties of anomalous diffusion and the critical and off-critical behavior of random quantum spin chains. Many exact results are obtained from this correspondence, including the space and time correlations of surviving random walks and the distribution of the gaps of the corresponding Fokker-Planck operator. In turn we derive analytically the dynamical exponent of the random transverse-field Ising spin chain in the Griffiths-McCoy region.