Equivalence of random and competing nonrandom bonds for Edwards Anderson spin-glass

We map the Edwards Anderson Hamiltonian onto an effective Hamiltonian for Ising spins with nonrandom competing couplings. A high-temperature series is used to calculate the coupling constants to 20th, 16th, and 12th order for two, three, and four dimensions, respectively. We conclude the lower critical dimension to be close to three and find the correlation-length and susceptibility critical exponents to be twice as large as for thed=3 Ising model.     

Pushing the envelope of the test functions in the Szegö and Avram–Parter theorems

The Szegö and Avram–Parter theorems give the limit of the arithmetic mean of the values of certain test functions at the eigenvalues of Hermitian Toeplitz matrices and the singular values of arbitrary Toeplitz matrices, respectively, as the matrix dimension goes to infinity. The question on whether these theorems are true whenever they make sense is essentially the question on whether they are valid for all continuous, nonnegative, and monotonously increasing test functions. We show that, surprisingly, the answer to this question is negative. On the other hand, we prove the two theorems in a general form which includes all versions known so far.     

Anion–π Interactions in Salts with Polyhalide Anions: Trapping of I42−

The directionality of interaction of electron‐deficient π systems with spherical anions (e.g,. halides) can be controlled by secondary effects like NH or CH hydrogen bonding. In this study a series of pentafluorophenyl‐substituted salts with polyhalide anions is investigated. The compounds are obtained by aerobic oxidation of the corresponding halide upon crystallization. Solid‐state structures reveal that in bromide 2 , directing NH–anion interactions position the bromide ion in an η¹‐type fashion over but not in the center of the aromatic ring. The same directing forces are effective in corresponding tribromide salt 3 . In the crystal, the bromide ion is paneled by four electron‐deficient aromatic ring systems. In addition, compounds 4 and 6 , which have triiodide and the rare tetraiodide dianion as anions, are described. Computational studies reveal that the latter is highly unstable. In the present case it is stabilized by the crystal lattice, for example, by interaction with electron‐deficient π systems.     

An organocatalytic approach to 2-hydroxyalkyl- and 2-aminoalkyl furanes

The first enantioselective methodology for the synthesis of electron-poor 2-hydroxyalkyl- and 2-aminoalkyl furanes is demonstrated in this study. It utilizes a highly stereoselective organocatalytic one-pot reaction cascade: epoxidation or aziridination of α,β-unsaturated aldehydes followed by Feist-Be?nary reaction of various 1,3-dicarbonyl compounds to give the target furanes. This efficient multibond forming reaction cascade benefits from low catalyst loadings and readily available starting materials. Furthermore, the possibility to interrupt the reaction sequence at the stage of the corresponding optically active 2-hydroxyalkyl- and 2-aminoalkyl 2,3-dihydrofuranes with three stereogenic centers is also presented. Finally, models which account for the formation of the optically active 2,3-dihydrofuranes are proposed.