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1.
Jean Bricmont Jean-Raymond Fontaine Eugene Speer 《Communications in Mathematical Physics》1982,86(3):337-362
We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /44 — /22 perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice
d
has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or 2) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920 相似文献
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Neutron diffraction has been used to study the whole structural evolution of the antimony oxide FeSb2O4, from 2 to 300 K. The antiferromagnetic order has been investigated: at 2 K the magnetic moment is M = 3.8 μB. An extrapolated Néel temperature TN = 45 ± 6 K is observed. The function M(T) below TN is similar to that found in the isomorphous NiSb2O4. Magnetostrictive effects are observed. Above 70 K, the thermal expansion tensor is anisotropic with αa ? αc. Using the anisotropic temperature factors Ba (Å2), Bc (Å2) at 2 and 300 K, anisotropic Debye temperatures are calculated. Then, using simple approximations, mean force constants Fa, Fc are calculated; they allow to evaluate the anisotropic compressibility coefficients χa ~ 0.857 × 10?11Pa?1, χc ~ 0.467 × 10?11Pa?1; the value of the Grüneisen constant is . 相似文献
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The structure of Pb3O4 at 293 K has been refined to an R value of 0.06, using 29 neutron diffraction data obtained from a powdered sample.Oxygen atoms are displaced in the quadratic cell (space group Å and c = 6.563 Å) with respect to previous results obtained by several authors. The interatomic PbIVO and PbIIO distances are compared with those found in other lead oxides. While the oxygen octahedra around PbIV atoms are characterized by bondings a little too long, the divalent lead coordination is characterized by bondings a little too short. 相似文献
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Pawel Nowakowski Sylvie Villain Jean-Raymond Gavarri 《Journal of solid state chemistry》2008,181(5):1005-1016
Nanostructured powders of ruthenium dioxide RuO2 were synthesized via a sol gel route involving acidic solutions with pH varying between 0.4 and 4.5. The RuO2 nanopowders were characterized by X-ray diffraction, scanning and transmission electron microscopy (SEM and TEM). Rietveld refinement of mean crystal structure was performed on RuO2 nanopowders and crystallized standard RuO2 sample. Crystallite sizes measured from X-ray diffraction profiles and TEM analysis varied in the range of 4-10 nm, with a minimum of crystallite dimension for pH=1.5. A good agreement between crystallite sizes calculated from Williamson Hall approach of X-ray data and from direct TEM observations was obtained. The tetragonal crystal cell parameter (a) and cell volumes of nanostructured samples were characterized by values greater than the values of standard RuO2 sample. In addition, the [Ru-O6] oxygen octahedrons of rutile structure also depended on crystal size. Catalytic conversion of methane by these RuO2 nanostructured catalysts was studied as a function of pH, catalytic interaction time, air methane composition, and catalysis temperature, by the way of Fourier transform infrared (FTIR) spectroscopy coupled to homemade catalytic cell. The catalytic efficiency defined as FTIR absorption band intensities I(CO2) was maximum for sample prepared at pH=1.5, and mainly correlated to crystallite dimensions. No significant catalytic effect was observed from sintered RuO2 samples. 相似文献
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Jean Bricmont Jean-Raymond Fontaine Joel L. Lebowitz Elliott H. Lieb Thomas Spencer 《Communications in Mathematical Physics》1981,78(4):545-566
We prove that the expansion in powers of the temperatureT of the correlation functions and the free energy of the plane rotator model on ad-dimensional lattice is asymptotic to all orders inT. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures ford=3.Supported by NSF Grant No. MCS 78-01885Supported by NSF Grant No. PHY 78-15920Supported by NSF Grant No. DMR 73-04355Supported by NSF Grant No. PHY-7825390 A01On leave from: Institut de Physique Théorique, Université de Louvain, BelgiumAlso: Department of Physics 相似文献
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Agnes Kopia-Zastawa I. Suliga A. Siwek J. Kusinski S. Villain M. A. Fremy M. H. Pischedda J. R. Gavarri 《Journal of solid state chemistry》2001,160(2):332
Solid state chemical evolutions are studied in the case of superconductor/ferrite composites as a function of time and temperature. Pellets have been fabricated from ferrite NiFe2O4 and superconducting cuprate Bi1.6Pb0.4Sr2Ca2Cu3O10+X (noted as Bi-2223). Two types of experimental approaches are presented: high-temperature electrical complex impedance spectroscopy, and EDAX analyses performed from scanning electron microscopy. From the in situ electrical analyses, two steps in the solid state chemical evolutions have been evidenced for the first time. They can be associated with two types of solid state reactions: (i) direct reactions between the ferrite phase and the superconducting matrix and (ii) a self-degradation of the superconducting phase probably associated with a homogenization of elements. The electrical analyses are modeled using two types of kinetics parameters. From the EDAX analyses, the local distribution of each element is determined. The concentration profiles found for the various elements (Ni, Fe, Bi, Sr, Ca, Cu) are interpreted in terms of a virtual diffusion law involving virtual D* coefficients. These coefficients are found to be of about 10−11 (cm2/s) in the range 800–830°C. 相似文献
8.
Jean Bricmont Jean-Raymond Fontaine Joel L. Lebowitz Thomas Spencer 《Communications in Mathematical Physics》1981,78(3):363-371
We consider perturbations of a massless Gaussian lattice field on ? d ,d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., $$ - H = \sum\limits_{< x,y > } {(\phi _x - \phi _y )^2 + T(\phi _x - \phi _y )^4 ,\phi _x \in \mathbb{R}.} $$ It is known that for allT>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities. 相似文献
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We give a simple estimate on the probability of contours in classical ferromagnetic spin systems, based on Griffiths' or Ginibre's correlation inequalities. This includes quite general one- and two-component spin models. Some extension also holds for alln-component anisotropic or isotropic rotators.Supported by NSF grant No. MCS78-01885.On leave from: Institut de Physique Théorique, Université de Louvain, Belgium.Supported by NSF grant No. PHY78-15920. 相似文献
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