Year: 2026
Type: article
Abstract: Controlled stochastic growth of structures in spatial domains is a fundamental challenge across many scientific disciplines, arising for example in biological pattern formation and solution-based crystallization. In this work, we consider controlled growth in a zero-temperature, two-dimensional Ising model on a finite square lattice evolving under Metropolis dynamics. We investigate how the system can be driven efficiently toward the all-plus configuration through external perturbations applied at predetermined times, starting from a configuration containing a small positive droplet. To analyze this control problem, we formulate it as a Markov decision process, a well-established framework for sequential decision-making under uncertainty. To find an approximately optimal strategy, we propose a reduction of the configuration space to the local minima of the Hamiltonian. Exploiting structural properties of this reduced model, we characterize the optimal policy by recursively solving the associated Bellman optimality equations. The resulting growth mechanism differs fundamentally from the typical evolution observed in the uncontrolled metastable regime. A simulation study demonstrates the effectiveness of this policy and shows that its performance persists at low but positive temperatures.
Institutions: University of Twente, Centrum Wiskunde & Informatica
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7134805790