The Ising model as a playground for the study of wetting and interface behavior

Study of the critical behaviour of three-dimensional Ising-like systems on the basis of the 6model with allowance for microscopic parameters: I. High-temperature region

“…For example, our numerical value β c ˜ (0) = 1.2649 or β c J = 0.211 [27] for the ρ 4 model in the case where the potential parameters correspond to the nearestneighbour interaction with the constant J accords with the value (β c J ) −1 = 4.5103 [34,35] or β c J = 0.221 654(1) [36] calculated using the high-temperature series data. Similar values are also obtained using the real-space RG method based on the cumulant expansion (β c J = 0.224 01 [37]) and the Monte Carlo method (β c J = 0.221 654 ± 0.000 006 [38], β c J = 0.221 6595 ± 0.000 0026 [39][40][41]). Liu and Fisher [42] preferred β c J = 0.221 692, 0.221 630, and 0.221 620 for the simple cubic Ising lattice and three selected values of the susceptibility exponent γ (γ = 1.250, 1.2395, and 1.237, respectively).…”

Magnetic behavior of a mixed Ising 3/2 and 5/2 spin model

“…They can qualitatively explain several aspects of the magnetic behavior of some molecular compounds, such as the independence of the critical temperature on the concentration of the different spins, the appearance of compensation temperatures in a certain range of concentration of the components [15,16], the increased coercivity at the compensation temperature [5,6,9], etc. Translated to latticegas language, such models can also represent complicated multi-species adsorption problems [17,18]. Mixed systems with higher spins have the added attraction of presenting a rich variety of critical and multicritical phenomena [19][20][21].…”

Surface transitions under confinement

“…We notice that both ferromagnetic (low concentration of species AB) and antiferromagnetic (high concentration of AB) behaviour is displayed by the phase properties of the mixture. We can study the inhomogeneous states of this mixture model in continuum space by considering the Landau density functional in equations ( 1) and (2) and by relating the bulk field h and the temperature difference t to the mixture chemical potentials via equations ( 8) and (9) with at = J −kT /2. The relationship between the magnetization m(z) and the densities of the mixture ρ AA (z), ρ BB (z) and ρ AB (z) is given by m(z) = ρ BB (z)−ρ AA (z).…”

“…In agreement with finite size scaling arguments there is a convergence of the coexistence curve and its associated critical point T (L) Parallel to this, the single effect of surface fields and coupling enhancements on phase behaviour, as described by the surface transitions and critical phenomena occurring in onewall semi-infinite systems, has been similarly developed [6,7]. A global phase diagram for the wetting, prewetting, pure surface and other transitions is known in detail from analysis based on the Landau phenomenological theory [8], and has been generally substantiated via numerical simulation studies [9]. For a simple system in magnetic language, the relevant thermodynamic field variables are: t the temperature difference to T (∞) c , h the bulk field, h 1 the surface field, and g the enhancement of interactions at the surface.…”