Work probability distribution for a ferromagnet with long-ranged and short-ranged correlations

TL;DR

This paper investigates how work probability distributions differ between systems with long-ranged and short-ranged correlations, using a ferromagnet model to analyze the crossover behavior as magnetic field varies.

Contribution

It provides a quantitative analysis of the crossover in work distributions in a ferromagnet transitioning from long- to short-range correlations by tuning magnetic field.

Findings

Work distribution is broader in long-ranged correlated systems.

Crossover behavior of work distribution is quantitatively characterized.

Implications for fluctuation theorems like Jarzynski are discussed.

Abstract

Work fluctuations and work probability distributions are fundamentally different in systems with short- ranged versus long-ranged correlations. Specifically, in systems with long-ranged correlations the work distribution is extraordinarily broad compared to systems with shortranged correlations. This difference profoundly affects the possible applicability of fluctuation theorems like the Jarzynski fluctuation theorem. The Heisenberg ferromagnet , well below its Curie temperature, is a system with long-ranged correlations in very low magnetic fields due to the presence of Goldstone modes. As the magnetic field is increased the correlations gradually become short-ranged. Hence, such a ferromagnet is an ideal system for elucidating the changes of the work probability distribution as one goes from a domain with long-ranged correlations to a domain with short-ranged correlations by tuning the magnetic field. A quantitative analysis of this crossover behaviour of the work probability distribution and the associated fluctuations is presented.