T. Hofsäss

Gaussian curvature in an Ising model of microemulsions

We extend Widom’s Ising‐like model of microemulsions on a simple cubic lattice by a new term which accounts for the Gaussian curvature energy of the oil–water interfaces. The new term distinguishes between different topologies of the interfaces and plays an important role in determining the microstructure of microemulsions on a scale larger or comparable to the persistence length provided that the microemulsion is dominated at all by curvature energies. We also speculate on its possible role for the breakdown of curvature energies in microemulsions.

A generalization of Widom’s model of microemulsions

We construct a generalization of Widom’s model of microemulsions which permits the contact of polar and apolar material. This is necessary to explain the behavior of certain short chain amphiphilic systems. The same interactions have previously been proposed by Robledo, but the partition function which he derived from these interactions and discussed in detail in his paper (a partition function of a spin 1 Ising system) does not quite represent these interactions. We arrive at a spin 3/2 Ising model with nearest neighbor interactions. Robledo’s spin 1 form is recovered as an approximation whose range of validity is discussed. We particularly investigate the limit towards Widom’s model, the progression of Winsor microemulsion, and the question of retrograde solubility in the binary water–amphiphile subsystem, which has been advocated by Robledo.

Field theory of self-avoiding random surfaces

Abstract We present and analyze a simple field theory whose partition function sums up all self-avoiding random surfaces with m internal degrees of freedom (“colors”). The field theory suggests that for m = 1 the critical indices are Ising like, while for m = 2 the transition falls into the universality class of the U(1) lattice gauge theory and the surfaces proliferate smoothly, the only phase transition lying at infinite temperature.

Thermal properties of defect melting

Abstract Using mean field theory and high temperature expansions the transition temperature, entropy jump and heat capacity are calculated in the recent microscopic model of defect melting proposed by Kleinert. The results are compared with the experimental data for almost isotropic substances.

Towards custom-made microemulsions

Abstract With the goal of finding the optimal properties of soaps used for tertiary oil recovery we show which properties control the position and shape of the three-phase regime in ternary mixtures of oil, water, and soap. We determine the conditions for the existence of large and multiple three-phase regimes in the phase prism formed by the Gibbs triangle of compositions and the temperature axis.

Simple lattice model for self-avoiding random loops

Abstract We show that the partition function of an ensemble of self-avoiding random loops Z = Σ loops β length can be reexpressed as a local lattice mmodel involving Ising spins. We present an approximation evaluation for D =2 and large β where the loops are prolific, and compare the results with Monte Carlo data obtained from a direct summation of random loops.

Field theory of self-avoiding random chains

Abstract We present a new lattice model whose partition function is equal to the sum over all self-avoiding closed random chains of m colors. The fluctuating variables are pure phases similar to an XY model and, contrary to previous proposals, no awkward n →0 limits are involved. The model can be transformed to a real O ( m ) invariant field theory, which shows that the critical indices are O( m ) like. There exists a simple relation to O( m ) spin models which serves to estimate the critical temperatures.

From self-avoiding random loops to Ising systems an interpolating spin model and its Monte Carlo study☆

Abstract We develop a new lattice model involving Ising spins on links with next-neighbor couplings which contains a parameter ξ that interpolates between the standard Ising model ( ξ =1) and an ensemble of self-avoiding random loops ( ξ =0). This model is studied by Monte Carlo techniques. We calculate the average length and its variance as a function of temperature. The reliability of our results is checked at several steps by comparison with the exactly known Ising case on finite lattices.

Disorder field theory of the ensemble of random loops without spikes

SummaryWe prove that a grand-canonical ensemble of random loops without spikes (i.e. without immediate backtrackcrs) obey afree disorder field theory with a mass parameter, on a simple cubic lattice,m2 = exp [ε/T] − 2D + (2D − 1) exp [− ε/T], where ε is the energy per link andD the spatial dimension. Thus the lines proliferate at a temperatureTc= ε/log(2D−1) as one might naively expect.

Are gluons composite? A new lattice gauge model with an exact U(∞) solution

Abstract The search for an exact N → ∞ solution of U( N ) gauge theories has led us to a new lattice model in which the gauge field dynamics is generated by four fundamental tensor fields describing subgluons. Our model has the same β → 0 limit as Wilsons and the same β → ∞ limit as far as the soft weak field excitations are concerned. It allows for the introduction of colorless Hartree like collective fields and has a simple N → ∞ solution.