Universal properties of Ising clusters and droplets near criticality

TL;DR

This paper investigates the universal properties of Ising model clusters and droplets near criticality, using integrable field theory to analyze amplitude ratios and their relation to percolative and magnetic universality classes.

Contribution

It introduces a theoretical framework to determine amplitude ratios for Ising clusters and droplets near criticality, highlighting differences between percolative and magnetic universality classes.

Findings

Percolative exponents match magnetic ones for droplets but differ for clusters.

Amplitude ratios characterize the approach to criticality within universality classes.

Integrable field theory effectively describes percolative critical behavior in the Ising model.

Abstract

Clusters and droplets of positive spins in the two-dimensional Ising model percolate at the Curie temperature in absence of external field. The percolative exponents coincide with the magnetic ones for droplets but not for clusters. We use integrable field theory to determine amplitude ratios which characterize the approach to criticality within these two universality classes of percolative critical behavior.