Critical behaviour of microemulsions: Monte Carlo simulations of the Widom model

Highlights: • The Widom lattice model for microemulsions is investigated by Monte Carlo simulation. • Histogram reweighting and finite size scaling methods are employed. • Critical behaviour of the model belongs to the 3D Ising universality class. • Critical amplitudes ratios are fully compatible with available theoretical predictions. -- Abstract: The critical behaviour of a lattice model for ternary mixtures of hydrophilic, hydrophobic and amphiphilic (surfactant) molecules is investigated by means of Monte Carlo simulations. A lattice model formulated by Widom as a simple approach of these mixtures is adopted taking advantage of its equivalence to a spin-$\frac{1}{2}$ Ising model, which adds next nearest neighbors interactions on a simple cubic lattice. In this work we focus on the critical behaviour of the order-disorder phase transition of this model. A simulation strategy combining a standard Metropolis sampling and multiple histogram reweighting technique is used. The location of the phase boundary is well determined, being consistent with the 3D Ising critical temperature. In addition, a suitable finite size scaling analysis is performed to obtain critical amplitudes of magnitudes as magnetization, susceptibility and interfacial tension. The critical behaviour results compatible with the 3D Ising universality class, as expected. Likewise, critical amplitudes ratios give a reasonable agreement with the universal values obtained from different systems and methods.