6.2.2. Definition of Effective Properties 3064 6.3. Response Properties to Magnetic Fields 3066 6.3.1. Nuclear Shielding 3066 6.3.2. Indirect Spin−Spin Coupling 3067 6.3.3. EPR Parameters 3068 6.4. Properties of Chiral Systems 3069 6.4.1. Electronic Circular Dichroism (ECD) 3069 6.4.2. Optical Rotation (OR) 3069 6.4.3. VCD and VROA 3070 7. Continuum and Discrete Models 3071 7.1. Continuum Methods within MD and MC Simulations 3072

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Quantum mechanical continuum solvation models.

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. It has moved into a central place in condensed matter studies. Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

Phase Transitions and Critical Phenomena

Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

/pdf/many-body-physics-with-ultracold-gases-552s10zfdn.pdf

Many-Body Physics with Ultracold Gases

A new definition of order called topological order is proposed for two-dimensional systems in which no long-range order of the conventional type exists. The possibility of a phase transition characterized by a change in the response of the system to an external perturbation is discussed in the context of a mean field type of approximation. The critical behaviour found in this model displays very weak singularities. The application of these ideas to the xy model of magnetism, the solid-liquid transition, and the neutral superfluid are discussed. This type of phase transition cannot occur in a superconductor nor in a Heisenberg ferromagnet.

https://iopscience.iop.org/article/10.1088/0022-3719/6/7/010/pdf

Ordering, metastability and phase transitions in two-dimensional systems

The partition function for a homogeneous plate of anisotropic elastic material is computed by solving an eigenvalue problem with realistic boundary conditions. The boundary contribution is separated by the approximation method which Dupuis, Mazo, and Onsager applied to the special case of an isotropic solid. The surface specific heat then is obtained as 

$$ {C_S} = 3\,\varsigma \,\left( 3 \right)\,\,\left( {{k^3}/{h^2}} \right)\,S\,{T^2}\,B\,\left( {\overrightarrow E ,\overrightarrow n } \right) $$

, where the proportionality factor B is determined by the elastic constants of the material and the orientation of the plate with respect to the crystallographic axes. Numerical examples of cubic and hexagonal systems (NaCl, MgO, Al, Graphite, Ice, Cd, and Mg) were computed. The surface specific heat data are plotted as functions of the orientation of the surface.

Lars Onsager

Papers

Surface Specific Heat of Crystals. I.

Low Temperature Fluctuations