A fixed-point equation for the high-temperature phase of discrete lattice spin systems

A fixed-point equation on an infinite-dimensional space is proposed as an alternative to the usual definition of the infinite-volume limit in discrete lattice spin systems in the high-temperature phase. It is argued heuristically that the free energy and correlation functions one obtains by solving this equation agree with the usual definitions of these quantities. A theorem is then proved that says that if a certain finite-volume condition is satisfied, then this fixed-point equation has a solution and the resulting free energy is analytic in the parameters in the Hamiltonian. For particular values of the temperature this finite-volume condition may be checked with the help of a computer. The two-dimensional Ising model is considered as a test case, and it is shown that the finite-volume condition is satisfied for0.77 _critical.     

Hamiltonian limit of the 3D Zamolodchikov model

A two-dimensional quantum Hamiltonian _N,M commuting with the layer-to-layer transfer matrix of the three-dimensional Zamolodchikov model is derived. This Hamiltonian is defined on a lattice ofN×M sites. The special casesN×2, 2×M, and 3×M are studied.This paper is dedicated to Cyril Domb.     

Dynamics of the current-driven Josephson junction

The irreversible macroscopic dynamics of the Josephson junction coupled to external wires acting as a current source is derived rigorously from the underlying microscopic Hamiltonian quantum mechanics. The external systems are treated in the singular coupling limit. The use of this limit is explicitly justified via an interpretation of the singular coupling limit in terms of the relative magnitudes of system, reservoir, and coupling energies. The qualitative behavior of the macroscopic dynamical equations is shown to depend sensitively and crucially on the interaction between the wires and the superconductors and on the size of the wires: the dc Josephson effect only happens when one lets Cooper pairs be driven into the junction by collective (i.e., small) reservoirs.     

无自旋混杂的耦簇理论

本文用APCCSD(T)，自旋投影方法消除CCSD中的自旋混杂，自旋投影算符^P用自旋湮灭算符^As 1和^As 2的乘积近似表出，提高了计算精度。     

Upper Bound to the Expectation Value of the Squared Hamiltonian

An upper bound to the expectation value of the squared Hamiltonian H ² is derived which relies on replacing products of certain operators with products of the matrix representations of said operators to reduce the computational demands of H ². An example is given which shows the strength of the bound and an application with the Temple lower bound is shown.     

Molecular structure of mixed adsorption layers surfactant—polymer at a liquid—liquid interface

Isotherms of the binding of dodecyl sulfate anions (DDS^–)and Na⁺ counterions during their coadsorption with a nonionic polymer. proxanol (PR). at the interface of dodecane-water emulsions have been measured by conductometry and Na-selective potentiometry. The adsorption of DDS^– and PR is concurrent. The affinity constant of PR to the interface determined by the Langmuir model decreases as the concentration of PR increases, and the surface concentration of DDS^– tends to a nonzero limiting value at high concentrations of PR. The surface (_o) and electrokinetic () potentials at the interface have been determined at various polymer concentrations by the spin probe and electrophoresis methods. The average dielectric permeability and density of polymer segments in We adsorption layer have been determined by ESR. The lower boundary of the hydrodynamic thickness of the polymer adsorption layer at the interface has been estimated from the dependences of _o and on the ionic strength.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1653–1661, July, 1996.     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

On the existence of thermodynamics for the generalized random energy model

Derrida's generalized random energy model is considered. Almost sure andL ^p convergence of the free energy at any inverse temperature are proven for an arbitrary numbern of hierarchical levels. The explicit form of the free energy is given in the most general case and the limitn is discussed.