Critical Droplets and Phase Transitions in Two Dimensions

TL;DR

This paper investigates how bond probability influences percolation and phase transition behavior in two-dimensional models, revealing a critical bond probability where percolation clusters become critical droplets of the phase transition.

Contribution

It demonstrates the existence of a critical bond probability in 2D models where percolation clusters transition to critical droplets, connecting percolation and thermal critical exponents.

Findings

Percolation point coincides with thermal critical point for p_B>=p_c.

At p_B=p_c, percolation exponents switch to thermal exponents.

Clusters at p_B=p_c act as critical droplets of the phase transition.

Abstract

In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing a bond probability p_B<1, the corresponding site-bond clusters keep on percolating at T_c and the exponents do not change, until p_B=p_CK=1-exp(-2J/kT): for this special expression of the bond weight the critical percolation exponents switch to the 2D Ising universality class. We show here that the result is valid for a wide class of bidimensional models with a continuous magnetization transition: there is a critical bond probability p_c such that, for any p_B>=p_c, the onset of percolation of the site-bond clusters coincides with the critical point of the thermal transition. The percolation exponents are the same for p_c<p_B<=1 but, for p_B=p_c, they suddenly change to the thermal exponents, so that the corresponding clusters are critical droplets of the phase transition. Our result is based on Monte Carlo simulations of various systems near criticality.