Multicolor particle systems with large threshold and range

In this paper we consider the Greenberg-Hastings and cyclic color models. These models exhibit (at least) three different types of behavior. Depending on the number of colors and the size of two parameters called the threshold and range, the Greenberg-Hastings model either dies out, or has equilibria that consist of debris or fire fronts. The phase diagram for the cyclic color models is more complicated. The main result of this paper, Theorem 1, proves that the debris phase exists for both systems.     

Random infinite-volume Gibbs states for the Curie-Weiss random field Ising model

An approach to the definition of infinite-volume Gibbs states for the (quenched) random-field Ising model is considered in the case of a Curie-Weiss ferromagnet. It turns out that these states are random quasi-free measures. They are random convex linear combinations of the free product-measures shifted by the corresponding effective mean fields. The conditional self-averaging property of the magnetization related to this randomness is also discussed.This paper is dedicated to Robert A. Minlos on the occasion of his 60th birthday.     

Monte carlo calculations of the conformal charge

The conformal charge is an important quantity which characterizes the nature of the two-dimensional phase transition. We report a first attempt to use a new numerical method to calculate the conformal charge. In this paper, we apply our method to the 2-dimensional, ⁴, continuous-spin Ising model. By varying the parameters in the Hamiltonian, one can change continuously from the known Gaussian limit to the Ising limit. It is well known that the critical points for these two systems are not in the same universality class. We study this behavior for the Gaussian model, the single-well ⁴ model, the border model, and the double-well ⁴ model for a large lattice. Our results, while giving a good general picture, are not so far sufficient to differentiate whether the non-Gaussian cases studied belong to the Ising model universality class or not. Further studies of other lattice sizes should serve to improve greatly our conclusions.     

Rigorous bounds on the storage capacity of the dilute Hopfield model

We study a neural network model consisting ofN neurons where a dendritic connection between each pair of neurons exists with probabilityp and is absent with probability 1-p. For the Hopfield Hamiltonian on such a network, we prove that ifp c[(lnN)/N]^1/2, the model can store at leastm= _cpN patterns, where _c 0.027 ifc 3 and decreases proportional to 1/(–lnc) forc small. This generalizes the results of Newman for the standard Hopfield model.     

Analyticity of the density of states in the anderson model on the Bethe lattice

Let H=1/2+V on l²(B), whereB is the Bethe lattice andV(x),x B, are i.i.d.r.v.'s with common probability distribution. It is shown that for distributions sufficiently close to the Cauchy distribution, the density of states(E) is analytic in a strip about the real axis.     

空间展布体系中由化学反应-扩散-热传导耦合导致的温度场对称破缺

分析了由于化学反应-扩散-热传导耦合而导致的非等温非均匀体系中温度场对称破缺.研究结果表明,在一定的边界条件下,甚至是单组分化学反应-扩散-热传导体系,温度场的这种自组织进程也不可避免.作为温度场结构的一个范例,进一步从解析解及计算机模拟两个方面研究了小展布非等温的Lindeman模型;结果表明,温度场出现时空自组织的阈值不仅与本征参数有关,而且与体系的边界条件及外控约束相关,揭示出了诱发或避免这种温度场时空自组织之途径.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

The discrete Gaussian chain with 1/r n interactions: Exact results

We show that the discrete Gaussian chain with interactionV(r) = 1/(r ²–1/4) is self-dual. At the dual temperaturek _B T = 1 we calculate the height-height correlation function and find that the system is rough. A duality relation is established for the temperature-dependent correlation function exponent. We also consider interactionsV(r)–1/r ⁿ and show that absence of a phase transition for 2 <n < 3 implies absence of a phase transition for 1 <n < 2. All these results have their counterparts in a linear system of charges interacting through a potential which is asymptotically logarithmic (forn = 2) or power-law-like (forn 2.On leave of absence from Chemistry Laboratory III, Universitetsparken 5, 2100 ©, Copenhagen, Denmark.     

Ionic conductivity of poly[N-(3,6,9-trioxadecyl)-4-vinylpyridinium)] salts with univalent counter-ions in aqueous solutions

In order to determine the counter-anion effect on conductivity of poly[N-(3,6,9-trioxadecyl)-4-vinylpyridinium)] backbone in aqueous solutions, a set of three polyelectrolytes with three different counter-ions: poly[N-(3,6,9-trioxadecyl)-4-vinylpyridinium]bromide P4VP164Br and its chlorate and tosylate derivatives P4VP164ClO₄ and P4VP164Ts respectively, were prepared by spontaneous polymerization of 4-vinylpyridine. This method gives a grafted polyelectrolyte having a positive charge on each pyridinic moiety on the backbone. The conductivities of cationic polyelectrolyte aqueous solution were determined in the concentration range from 10⁻⁴ to 10⁻² M at 25 °C. The variation of the conductivity versus concentration of the investigated system exhibits a typical polyelectrolyte behavior. The polycation mobility was found to be dependent on the counter-anion nature. Thus, the polyelectrolyte conductivity increases with the ion size. This shows that big ions are weakly or not associated to the backbone.In order to confirm this steric hindrance, we have considered the conductivities of these three anions Br⁻, ClO₄⁻ and Ts⁻ in their sodium salts, both alone and in the presence of 3,6,9-trioxadecanol (PEO164) free chains. In the two cases, the conductivities decrease in the order Λ_Br>Λ_ClO4>Λ_Ts.These results suggest that counter-ion mobility is mainly influenced by steric effect PEO164 grafted chains.Values of the conductivity predicted from Manning rod-like polyelectrolyte model were compared with our experimental results.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.