On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts

A theory is developed for the potential distribution around a charged spherical colloidal particle carrying ionized groups on the particle surface in a medium containing its counterions (i.e., counterions produced from dissociation of the particle surface groups) and a small amount of added salts on the basis of the theory of Imai and Oosawa. Numerical solutions to the Poisson–Boltzmann equation for the potential distribution are obtained for the case of dilute (but not infinitely dilute) particle suspensions of volume fraction 1 for a1 (where is the Debye–Hückel parameter and a is the particle radius). Here we have taken into account the effects of (i) counterions from the particle surface groups, and (ii) the finite particle volume fraction. These effects, which are usually neglected in the conventional Poisson–Boltzmann equation, are found to be important. It is found that, as in the case of completely salt-free media, there is a certain critical value of the particle charge (which is the same as that for the completely salt-free case). When the particle charge is lower than the critical value, the potential is given by a Coulomb potential. If the particle charge is higher than the critical value, then counterions are accumulated in the vicinity of the particle surface (counterion condensation) and the potential becomes less dependent on the particle charge. The above behaviors can be observed even for the case where the electrolyte concentration is higher than the concentration of counterions from the particle surface groups, if the conditions 1 and a1are both satisfied.     

The Effects of Beating,Web Forming and Sizing on the Surface Energy of <Emphasis Type="Italic">Eucalyptus globulus</Emphasis> Kraft Fibres Evaluated by Inverse Gas Chromatography

In this work attention has been focused on the effects of papermaking beating, web forming and sizing operations on the physical/chemical surface properties of bleached Eucalyptus globulus kraft fibres. Inverse gas chromatography (IGC) was used to determine the dispersive component of surface tension (γ_s^d) as well as the acidic/basic character (according to the Lewis concept) of the solid surfaces (pulp fibres and pulp handsheets). The results have shown that the main effect of beating is to increase the fibre's Lewis acidic character. Web forming caused a strong decrease in γ_s^d and significant increments in the adhesion works of both acidic and basic probes, lowering the ratio between the two. Nevertheless, the surface of handsheets still exhibited a dominant acidic character. The sizing operation did not change the dispersive component of the surface tension significantly but decreased the difference between the adhesion works of the acidic and basic probes, rendering the handsheet surface less Lewis acidic and more Lewis basic. Thus, although internal sizing is expected to strongly influence liquid spreading at the paper surface and liquid penetration of the fibre's network, it is concluded that beating and web forming lead to important changes in the surface energetic properties of the Eucalyptus globulus kraft fibres.     

ToF-SIMS analysis of surface-anchored organometallic clusters

ToF-SIMS analysis of the organometallic cluster Os₃(μ-H)(CO)₁₀(μ-SCH₂CH₂SH) chemically attached onto a silver or gold surface, and of the cluster fragment Os₃(μ-H)(CO)₁₀(μ-OSi) on a silica surface, allows for identification of the surface organometallic species, and also gives information on its reactivity.     

Adsorption of water molecules in slit pores

We report molecular dynamics (MD) simulations on the adsorption of water in attractive and repulsive slit pores, where the slit and a bulk region are in contact with each other. Water structure, surface force and adsorption behavior are investigated as a function of the overall density in the bulk region. The gas–liquid transition in both types of pores occurs at similar densities of the bulk region.     

Operator Semigroup Compactifications

A weakly continuous, equicontinuous representation of a semitopological semigroup on a locally convex topological vector space gives rise to a family of operator semigroup compactifications of , one for each invariant subspace of . We consider those invariant subspaces which are maximal with respect to the associated compactification possessing a given property of semigroup compactifications and show that under suitable hypotheses this maximality is preserved under the formation of projective limits, strict inductive limits and tensor products.

     

The covariance matrix of the Potts model: A random cluster analysis

We consider the covariance matrix,G ^mm =q ²<(_x,m);(_y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point _o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at _o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure.     

Generalized logic and the representation of rings

Following the progression towards weaker logics, a number of authors have considered the notion of a sheaf over a quantale or, equivalently, a quantale valued set. In this paper, we use ideas from enriched category theory to motivate the definition of a quantic sheaf. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.     

The occupation measure of super-Brownian motion conditioned to nonextinction

We study super-Brownian motion inR ^d starting from a nontrivial finite measure and conditioned to nonextinction as defined by Evans. If (Y _t ) _t0 denotes this process, we provide a new approach to the immortal particle representation of (Y _t ) _t0 . We then show that the measureZ onR ^d defined byZ(B)= _o ¹ Y _t (B) dt is almost surely finite on compact sets whend5 and almost surely infinite on every ball whend4.     

Series representation for semistable laws and their domains of semistable attraction

If the centered and normalized partial sums of an i.i.d. sequence of random variables converge in distribution to a nondegenerate limit then we say that this sequence belongs to the domain of attraction of the necessarily stable limit. If we consider only the partial sums which terminate atk _n wherek _n+1 ck _n then the sequence belongs to the domain of semistable attraction of the necessarily semistable limit. In this paper, we consider the case where the limiting distribution is nonnormal. We obtain a series representation for the partial sums which converges almost surely. This representation is based on the order statistics, and utilizes the Poisson process. Almost sure convergence is a useful technical device, as we illustrate with a number of applications.This research was supported by a research scholarship from the Deutsche Forschungsgemeinschaft (DFG).