Construction of an effective Hamiltonian for a three-dimensional Ising universality class

Smooth cutoff formulation of hierarchical reference theory for a scalar phi4 field theory

The phi4 scalar field theory in three dimensions, prototype for the study of phase transitions, is investigated by means of the hierarchical reference theory (HRT) in its smooth cutoff formulation. The critical behavior is described by scaling laws and critical exponents which compare favorably with the known values of the Ising universality class. The inverse susceptibility vanishes identically inside the coexistence curve, providing a first principle implementation of the Maxwell construction, and shows the expected discontinuity across the phase boundary, at variance with the usual sharp cutoff implementation of HRT. The correct description of first and second order phase transitions within a microscopic, nonperturbative approach is thus achieved in the smooth cutoff HRT.

Microscopic approach to critical phenomena at interfaces: an application to complete wetting in the Ising model

We study how the formalism of the hierarchical reference theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid-state theory which implements the basic ideas of the Wilson momentum-shell renormalization group (RG) to microscopic Hamiltonians. In the case of homogeneous systems, HRT provides accurate results even in the critical region, where it reproduces scaling and nonclassical critical exponents. We applied the HRT to study wetting critical phenomena in a planar geometry. Our formalism avoids the explicit definition of effective surface Hamiltonians but leads, close to the wetting transition, to the same renormalization group equation already studied by RG techiques. However, HRT also provides information on the nonuniversal quantities because it does not require any preliminary coarse graining procedure. A simple approximation to the infinite HRT set of equations is discussed. The HRT evolution equation for the surface free energy is numerically integrated in a semi-infinite three-dimensional Ising model and the complete wetting phase transition is analyzed. A renormalization of the adsorption critical amplitude and of the wetting parameter is observed. Our results are compared to available Monte Carlo simulations.

Ising fluids in an external magnetic field: an integral equation approach

The phase behavior of Ising spin fluids is studied in the presence of an external magnetic field with the integral equation method. The calculations are performed on the basis of a soft mean spherical approximation using an efficient algorithm for solving the coupled set of the Ornstein-Zernike equations, the closure relations, and the external field constraint. The phase diagrams are obtained in the whole thermodynamic space including the magnetic field H for a wide class of Ising fluid models with various ratios R of the strengths of magnetic to nonmagnetic Yukawa-like interactions. The influence of varying the inverse screening lengths z(1) and z(2), corresponding to the magnetic and nonmagnetic Yukawa parts of the potential, is investigated too. It is shown that changes in R as well as in z(1) and z(2) can lead to different topologies of the phase diagrams. In particular, depending on the value of R, the critical temperature of the liquid-gas transition either decreases monotonically, behaves nonmonotonically, or increases monotonically with increasing H. The para-ferro magnetic transition is also affected by changes in R and the screening lengths. At H=0, the Ising fluid maps onto a simple model of a symmetric nonmagnetic binary mixture. For H--> infinity, it reduces to a pure nonmagnetic fluid. The results are compared with available simulations and the predictions of other theoretical methods. It is demonstrated that the mean spherical approximation appears to be more accurate compared with mean field theory, especially for systems with short ranged attraction potentials (when z(1) and z(2) are large). In the Kac limit z(1), z(2) -->+0, both approaches tend to nearly the same results.