Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: A comparison for elastic flexible polymers

TL;DR

This paper compares two advanced methods, Fisher partition function zeros and microcanonical inflection-point analysis, for accurately identifying transition points in finite elastic polymers, demonstrating their consistency and effectiveness over traditional approaches.

Contribution

It systematically evaluates and compares the effectiveness of Fisher zeros and microcanonical inflection-point analysis for finite polymer transitions, highlighting their agreement and advantages.

Findings

Both methods yield similar transition temperatures.

They enable unique transition point identification in finite systems.

Advanced sampling techniques provide accurate density of states.

Abstract

For the estimation of transition points of finite elastic, flexible polymers with chain lengths from $13$ to $309$ monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.