Classification of Phase Transitions by Microcanonical Inflection-Point Analysis

TL;DR

This paper extends the microcanonical inflection-point analysis method to better identify phase transitions of any order in complex systems, demonstrated through applications to magnetic and polymer models.

Contribution

It introduces a generalized approach using entropy derivatives to systematically detect and classify phase transitions of all orders.

Findings

Successfully applied to Ising model and polymer adsorption system

Revealed detailed phase structure and transition signals

Enhanced understanding of cooperative behavior in complex systems

Abstract

By means of the principle of minimal sensitivity we generalize the microcanonical inflection-point analysis method by probing derivatives of the microcanonical entropy for signals of transitions in complex systems. A strategy of systematically identifying and locating independent and dependent phase transitions of any order is proposed. The power of the generalized method is demonstrated in applications to the ferromagnetic Ising model and a coarse-grained model for polymer adsorption onto a substrate. The results shed new light on the intrinsic phase structure of systems with cooperative behavior.