Random walks interacting with evolving energy landscapes

TL;DR

This paper presents a novel diffusion model where a random walker interacts with and influences a dynamic Ising energy landscape, revealing phase transition signatures through coupled spin and walk dynamics.

Contribution

It introduces a coupled diffusion-spin model where the walker modifies the energy landscape, providing new insights into phase transitions in inhomogeneous systems.

Findings

Walker bias towards high energy regions at cluster boundaries

Coupling effects depend on temperature and spin magnitude

Model captures signatures of phase transitions

Abstract

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.