Phase boundaries near critical end points. III. Corrections to scaling and spherical models

Three-dimensional Ising model with nearest- and next-nearest-neighbor interactions

The phase diagram of the Ising model in the presence of nearest- and next-nearest-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by employing an effective-field theory with finite clusters consisting of a pair of spins. A functional form is also proposed for the free energy, similar to the Landau expansion, in order to obtain the phase diagram of the model. The transition from the ferromagnetic (or antiferromagnetic) phase to the disordered paramagnetic phase is of second order. On the other hand, a first-order transition is obtained from the lamellar phase to the paramagnetic phase, as well as from the lamellar phase to the ferromagnetic (or antiferromagnetic) phase, with the presence of a critical end point. An expected singular behavior of the first-order line at the critical end point is also obtained.

Critical endpoint behavior in an asymmetric Ising model: application of Wang-Landau sampling to calculate the density of states

Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.

Universality and double critical end points

A double critical end point in the two-dimensional spin-3/2 Blume-Capel model is studied via extensive Monte Carlo simulations. The resultant scaling character of the probability distribution of the mixing scaling operators allows us to locate the double critical end point precisely and also to convincingly show that it indeed belongs to the same universality class as the critical points.

Phase diagram of symmetric binary fluid mixtures: first-order or second-order demixing

Binary fluid mixtures of 1:1 concentration can demix in a phase transition of first order or of second order. We analyze the two scenarios in density-concentration space and relate them to the structure of the line at which the demixing coexistence surface cuts the liquid-vapor coexistence surface. These scenarios help us to decide between first and second order for a model of a symmetric Lennard-Jones mixture. An optimized reference hypernetted chain integral equation method is employed for calculating the correlation functions and from there the pressure and chemical potentials. We conclude that demixing of a 1:1 mixture is of first order in the whole range of parameters that we have investigated. We did not find a critical point in the 1:1 concentration plane.