We develop a resummed high-temperature expansion for lattice spin systems with long range interactions, in models where the free energy is not, in general, analytic. We establish uniqueness of the Gibbs state and exponential decay of the correlation functions. Then, we apply this expansion to the Perron-Frobenius operator of weakly coupled map lattices.

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean eld type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translationinvariant interactions of nite range. In the spe...

This paper addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed for homogeneous materials with constant...

The heat of fusion and the specific heats of the solid and liquid have been experimentally determined for a Ti6&r4a alloy. The data are used to evaluate the Gibbs free energy difference, AG, between the liquid and the 0 phase as a function of temperature to verify a reported spontaneous vitrification (SV) of the fi phase in Ti-Cr alloys. The results show that SV of an undistorted fl phase in th...

Activation of CO2 is demonstrated by its spontaneous dissociative reaction with the gas-phase anion complex NUOCl2(-), which can be considered as NUO(+) coordinated by two chloride anion ligands. This reaction was previously predicted by density functional theory to occur exothermically, without barriers above the reactant energy. The present results demonstrate the validity of the prediction o...

Abstract. – We consider the statistical mechanics of a classical particle in a onedimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation functions of the Gibbs states may be calculated exactly as a function of the box length and temperature. This allows for a detailed test of results obta...

Abstract. The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when βt is small, or βt/U is small; here, β is the inverse temperature, U the on-site repulsion and t the hopping coefficient. For more general models with Hamiltonian H = V +T where V involves local terms only, the free energy is analytic when β‖T ‖ is smal...

Black lipid membranes (BLM) less than 90 A thick have been shown to be the most realistic approach to biological membrane models. This paper describes the formation characteristics, optical properties, and thermodynamics of BLM at water/oil/water bifaces. In particular, the nature of the Plateau-Gibbs border which supports the black membrane is analyzed in some detail. The formation of BLM at t...

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translationinvariant interactions of finite range. In the...

The application of cerium oxide nanoparticles (CNPs) for therapeutic purposes requires a stable dispersion of nanoparticles in a biological environment. The objective of this study is to tailor the properties of polyelectrolyte coated CNPs as a function of molecular weight to achieve a stable and catalytic active dispersion. The coating of CNPs with polyacrylic acid (PAA) has increased the disp...