A novel approach to the study of critical systems

TL;DR

This paper introduces a new method based on instantaneous correlation length to analyze critical behavior in various systems, successfully distinguishing phase transition types and revealing surprising criticality in the forest fire model.

Contribution

It presents a novel approach to studying critical phenomena that effectively characterizes phase transitions and uncovers unexpected criticality in self-organized criticality models.

Findings

Successfully characterizes critical behavior in XY and Ising models.

Discriminates between different types of phase transitions.

Reveals potential criticality in the forest fire model despite broken scaling.

Abstract

We introduce a novel approach to study the critical behavior of equilibrium and non-equilibrium systems which is based on the concept of an instantaneous correlation length. We analyze in detail two classical statistical mechanical systems: the XY model and the Ising model, and one of the prototype models of Self-Organized Criticality: the forest fire model (FFM). The proposed method can both capture the critical behavior of the XY model and the Ising model and discriminate between the nature of the phase transition in the two scenarios. When applied to the FFM, it gives surprising results, suggesting that the model could be critical despite displaying broken scaling in the distribution of cluster sizes.