Random walks interacting with evolving energy landscapes
Università degli Studi di Parma, Parco Area delle Scienze 7/a, 43100 Parma, Italy
2 Istituto Nazionale Fisica della Materia (INFM), UdR PARMA, Parco Area delle Scienze 7/a, 43100 Parma, Italy
Corresponding author: a email@example.com
Published online: 19 January 2006
We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying energetic environment is also made dynamic by properly coupling the walker with the spin lattice. In fact, while the walker hops across nearest-neighbor sites, it can flip the pertaining spins, realizing a diffusive dynamics for the Ising system. As a result, the walk is biased towards high energy regions, namely the boundaries between clusters. Besides, the coupling introduced involves, with respect the ordinary diffusion laws, interesting corrections depending on either the temperature and the spin magnitude. In particular, they provide a further signature of the phase-transition occurring on the magnetic lattice.
PACS: 5.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.40.Fb – Random walks and Levy flights / 05.60.-k – Transport processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006