Percolation of random clusters and the nature of percolation in the 2D ±J random bond Ising Model

Fortuin--Kasteleyn, AKA random cluster representation played an important role in developing efficient algorithms for simulating unfrustrated Ising and Potts models since it allows for non-local spin configuration updates. A crucial property of random clusters, which underpins this approach is that their percolation coincides with the onset of spontaneous magnetization. This is, however, no longer the case once the spin system is frustrated. Even a small concentration of antiferromagnetic bonds leads to a separation between the percolation and magnetic transitions, with the former occurring at a higher temperature. The question then arises: What is the nature of the phase characterized by the onset of percolation of random clusters and absence of spontaneous magnetization? We attempt to address this question using Monte Carlo simulations and exploring the dynamical properties of the intermediate phase using Glauber relaxation dynamics.