Shape and interfacial structure of droplets. Exact results and simulations

We consider the fluctuating interface of a droplet pinned on a flat wall. For such a system we compare results obtained within the exact field theory of phase separation in two dimensions and Monte Carlo (MC) simulations for the Ising model. The interface separating coexisting phases splits and hosts drops whose effect is to produce subleading corrections to the order parameter profile and correlation functions. In this paper we establish the first direct measurement of interface structure effects by means of high-performance MC simulations which successfully confirm the field-theoretical results. Simulations are found to corroborate the theoretical predictions for interface structure effects whose analytical expression has recently been obtained. It is thanks to these higher-order corrections that we are able to correctly resettle a longstanding discrepancy between simulations and theory for the order parameter profile. In addition, our results clearly establish the long-ranged decay of interfacial correlations in the direction parallel to the interface and their spatial confinement within the interfacial region also in the presence of a wall from which the interface is entropically repelled.