Thermal statistics of small magnets

TL;DR

This paper investigates the limitations of the canonical ensemble in describing small magnetic systems, revealing significant deviations near critical points and proposing a superstatistical approach for improved accuracy.

Contribution

It demonstrates the failure of the canonical ensemble for small Ising magnets near criticality and introduces a superstatistical framework to better model their thermal behavior.

Findings

Significant deviations from canonical behavior near critical points.

Decoupling between system and bath influences statistical agreement.

Superstatistics improves modeling accuracy over Gibbs-Boltzmann.

Abstract

While the canonical ensemble has been tremendously successful in capturing thermal statistics of macroscopic systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a small two dimensional Ising magnet embedded inside a larger Ising magnet 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 of the two dimensional Ising model. Notably, the agreement with the canonical ensemble is driven not by the system size but by the statistical 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 its thermal statistics with significantly higher accuracy than the Gibbs-Boltzmann distribution. We discuss future directions.