Thermal behavior of small magnets

Abstract

While the canonical ensemble has been tremendously successful in capturing statistical properties of large systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a two-dimensional small Ising magnet embedded inside a larger heat bath, we characterize the failures of the canonical ensemble when describing small systems. We find significant deviations from the canonical behavior for small systems near and below the critical point. Notably, the agreement with the canonical ensemble is driven not by the system size but by the decoupling between the system and its surrounding. A superstatistical framework wherein we allow the temperature of the small magnet to vary is able to capture the statistics of the small magnet with significantly higher accuracy than the Gibbs–Boltzmann distribution. We discuss implications for experiments and future directions.