Low temperature expansion for continuous-spin Ising models

We consider general ferromagnetic spin systems with finite range interactions and an even single-spin distribution of compact support on IR. It is shown under mild assumptions on the single-spin distribution that a low temperature expansion, in powers ofT, for the free energy and the correlation functions is asymptotic. We also prove exponential clustering in the pure phases and analyticity of the free energy and of the correlation functions in the reciprocal temperature for Re large.Supported in part by N.S.F. Grant No. Phy. 78-15920 and MCS 78-01885On leave from: Départment de Physique Théorique, Université de Louvin, BelgiumSupported in part by the Swiss National Foundation for Scientific Research     

Zur Kenntnis der Chemie der Metallcarbonyle und der Cyanokomplexe in flüssigem Ammoniak. XXXI. Über die Reaktionen von kationischen η5-Cyclopentadienylmolybdäncarbonyl-Komplexen mit flüssigem Ammoniak

The Chemistry of Metal Carbonyls and Cyano Complexes in Liquid Ammonia. XXXI. On the Reactions of Cationic η⁵-Cyclopentadienyl-molybdenumcarbonyl Complexes with Liquid Ammonia Depending on the reaction conditions, the cationic complexes [η⁵-C₅H₅Mo(CO)₃L]⁺ (L = NH₃, PPh₃, CO) react with liquid ammonia according to: The characteristics and reactivities of the new carbomoyl derivatives are described.     

On classical ferromagnets with a complex external field

We prove analyticity properties of correlation functions using correlation inequalities.     

On the symmetry of the Gibbs states in two dimensional lattice systems

Under fairly general conditions if a two dimensional classical lattice system has an internal symmetry groupG, which is a compact connected Lie group, then all Gibbs states areG-invariant.     

Zur Kenntnis der Chemie der Metallcarbonyle und der Cyanokomplexe in flüssigem Ammoniak. XXXII. Über die Reaktionen von η5-C5H5Mo(CO)3CH3 und η5-C5H5Fe(CO)2CH3 mit flüssigem Ammoniak

The Chemistry of Metal Carbonyls and Cyano Complexes in Liquid Ammonia. XXXII. On the Reaction of η⁵-C₅H₅Mo(CO)₃CH₃ and η⁵-C₅H₅Fe(CO)₂CH₃ with Liquid Ammonia η⁵-C₅H₅Mo(CO)₃CH₃ reacts with liquid NH₃ to give η⁵-C₅H₅Mo(CO)₂(NH₃)H and acetamide: In contrast, η⁵-C₅H₅Fe(CO)₂CH₃ undergoes a carbonyl insertion to give the acetyl complex η⁵-C₅H₅Fe(CO)(NH₃)COCH₃: The NH₃ ligand in η⁵-C₅H₅Fe(CO)(NH₃)COCH₃ can be substituted by pyridine.     

Application of the smiles rearrangement to the synthesis of 5,7-disubstituted xanthone-2-carboxylic acids

The depside-like esters 3a and 3b underwent a Smiles rearrangement on treatment with base. The resulting diphenyl ethers 4a and 4b were converted into the xanthonecarboxylic acids 6a and 6b which are not readily accessible by other routes.     

Copper‐Mediated ortho‐Nitration of (Hetero)Arenecarboxylates

Various (hetero)arenecarboxylic acids were converted to the corresponding Daugulis amides and nitrated selectively in the ortho‐position in the presence of [CuNO₃(PPh₃)₂] and AgNO₂ at 50 °C. A microwave‐assisted saponification allows regenerating the carboxylate group within minutes, which may then be removed tracelessly by protodecarboxylation, or substituted by aryl‐ or alkoxy‐groups via decarboxylative cross‐coupling.     

Semi-infinite Ising model

For the semi-infinite Ising model in two or more dimensions, we prove analyticity properties of the surface free energy and map out the phase diagram in the absence of an external magnetic field. We prove that this phase diagram contains critical lines where the parallel and/or the transverse correlation lengths diverge. The critical exponent,v _⊥, of the transverse correlation length is shown to be equal to the exponentv of the Ising model on an infinite lattice. In a second paper, these results will be used to analyze the wetting transition.     

Experiments on the interaction of current channels in a laboratoryplasma: relaxation to the force-free state

A series of experiments on the dynamic interaction of two current channels has been performed in the large plasma device, a laboratory device at UCLA. The two current channels are formed by coating the cathode source nonuniformly and then biasing it with respect to an anode 10 m away. The experiment consists of two phases, one in which a net current is drawn through the plasma, and one in which the net current is zero. The current channels twist about each other, merge, and evolve toward a force-free state when a net current is drawn through the plasma. When the net current is zero the interaction between the channels is greatly reduced. The dynamics of the system are dominated by electron pressure and associated electrostatic fields. However, as the currents twist, a small amount of magnetic helicity is generated. The helicity and its temporal rate of change are computed and found to compare within experimental uncertainty to the predicted rate     

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