Magnetic Properties of Finite Systems: Microcanonical Finite Size Scaling

TL;DR

This paper develops a microcanonical finite-size scaling theory that reveals non-analyticities and power-law behaviors in finite systems, aiding the understanding of critical phenomena.

Contribution

It introduces a novel finite-size scaling framework within the microcanonical ensemble for finite systems approaching criticality.

Findings

Observables exhibit non-analyticities in finite systems.

Power-law behaviors are present even for small systems.

The theory helps estimate critical exponents from finite data.

Abstract

In the microcanonical ensemble, suitably defined observables show non-analyticities and power law behaviour even for finite systems. For these observables, a microcanonical finite-size scaling theory is established which facilitates an approach to the critical exponents of the infinite system.