Finite-size behaviour of the microcanonical specific heat

TL;DR

This paper investigates the unusual finite-size effects of the microcanonical specific heat in models with continuous phase transitions, contrasting it with canonical ensemble behavior and proposing a phenomenological theory.

Contribution

It introduces a phenomenological theory to explain non-monotonic finite-size behavior of microcanonical specific heat and suggests a method to determine microcanonical critical exponents.

Findings

Microcanonical specific heat shows non-monotonic size dependence.

Canonical specific heat maximum increases monotonically with system size.

A phenomenological model describes the peculiar behavior of microcanonical specific heat.

Abstract

For models which exhibit a continuous phase transition in the thermodynamic limit a numerical study of small systems reveals a non-monotonic behaviour of the microcanonical specific heat as a function of the system size. This is in contrast to a treatment in the canonical ensemble where the maximum of the specific heat increases monotonically with the size of the system. A phenomenological theory is developed which permits to describe this peculiar behaviour of the microcanonical specific heat and allows in principle the determination of microcanonical critical exponents.