Structure of interfaces at phase coexistence. Theory and numerics

We compare results of the exact field theory of phase separation in two dimensions with Monte Carlo simulations for the q-state Potts model with boundary conditions producing an interfacial region separating two pure phases. We confirm in particular the theoretical predictions that below critical temperature the surplus of non-boundary colors appears in drops along a single interface, while for q > 4 at critical temperature there is formation of two interfaces enclosing a macroscopic disordered layer. These qualitatively different structures of the interfacial region can be discriminated through a measurement at a single point for different system sizes

Spin clusters and conformal field theory

We study numerically the fractal dimensions and the bulk three-point connectivity for spin clusters of the Q-state Potts model in two dimensions with 1 <= Q <= 4. We check that the usually invoked correspondence between FK clusters and spin clusters works at the level of fractal dimensions. However, the fine structure of the conformal field theories describing critical clusters first manifests at the level of the three-point connectivities. Contrary to what was recently found for FK clusters, no obvious relation emerges for generic Q between the spin cluster connectivity and the structure constants obtained from analytic continuation of the minimal model constants. The numerical results strongly suggest that spin and FK clusters are described by conformal field theories with different realizations of the color symmetry of the Potts model