Critical-point finite-size scaling in the microcanonical ensemble

TL;DR

This paper develops a finite-size scaling theory for the microcanonical entropy near critical points, linking it to canonical energy distributions and highlighting the role of background contributions, with validation in the 3d Ising model.

Contribution

It introduces a new scaling framework for microcanonical entropy at criticality, accounting for background effects, and confirms predictions using the 3d Ising universality class.

Findings

Scaling behavior emerges when background effects are considered.

Background constant influences differences between canonical and microcanonical specific heats.

The theory is corroborated in the 3d Ising model.

Abstract

We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.