Microcanonical scaling in small systems

TL;DR

This paper introduces a microcanonical finite-size scaling approach that accurately determines critical exponents for small systems without prior knowledge of the infinite system's critical point, enhancing understanding of phase transitions.

Contribution

It presents a novel microcanonical finite-size scaling ansatz that allows extraction of critical exponents without knowing the infinite system critical point.

Findings

Achieves good data collapse for small systems

Yields critical exponents consistent with other methods

Does not require the exact location of the infinite system critical point

Abstract

A microcanonical finite-size scaling ansatz is discussed. It exploits the existence of a well-defined transition point for systems of finite size in the microcanonical ensemble. The best data collapse obtained for small systems yields values for the critical exponents in good agreement with other approaches. The exact location of the infinite system critical point is not needed when extracting critical exponents from the microcanonical finite-size scaling theory.