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

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.

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Spintronics: Fundamentals and applications

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.

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Many-Body Physics with Ultracold Gases

An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of $^{4}\mathrm{He}$.

Theory of Dynamic Critical Phenomena

The Yang–Yang relation expresses the heat capacity at constant volume, CV(T,ρ), of a fluid linearly in terms of the second temperature derivatives of the pressure and the chemical potential, p″(T,ρ) and μ″(T,ρ). At a gas–liquid critical point CV diverges so, on approaching Tc from below, either pσ″(T), or μσ″(T), or both must diverge, where the subscript σ denotes the evaluation of p and μ on the phase boundary or vapor-pressure curve. However, previous theoretical and experimental studies have suggested that μσ″(T) always remains finite. To test these inferences, we present an analysis of extensive two-phase heat capacity data for propane recently published by Abdulagatov and co-workers. By careful interpolation in temperature and subsequently making linear, isothermal fits vs specific volume and vs density, we establish that the divergence is shared almost equally between the derivatives pσ″(T) and μσ″(T). A re-examination of the analysis of Gaddy and White for carbon dioxide leads to similar conclusions although the singular contribution from μσ″(T) is found to be of opposite sign and probably somewhat smaller than in propane.

The Yang–Yang relation and the specific heats of propane and carbon dioxide

The definitions and determination of the thermodynamic magnetic critical point exponents α, α′, β, γ, γ′ and δ are reviewed, and ``gap exponents'' Δ and Δ′ for the divergences of higher derivatives of the free energy with respect to the field are introduced. The rigorous inequalities relating the exponents are discussed.The ``microdomain'' or ``cluster'' model of ferromagnetism leads to relations between these exponents since it expresses them in terms of two underlying exponents σ and τ. The exponent σ is directly related to the effective surface free energy of a large microdomain and thence to the dimensionality. This yields some insight into the meaning of the observed exponent values and of the differences between the critical behavior of the Ising and Heisenberg models. The recently developed homogeneity and scaling arguments are presented. These generate the same thermodynamic exponent relations and further ones for the correlation exponents η, ν and ν′. They also indicate that a general law of corresponding states might hold in the critical region. Theoretical and experimental evidence on the validity of these various ideas is briefly reviewed.

Magnetic Critical Point Exponents—Their Interrelations and Meaning

Antiferromagnetic susceptibility of the plane square and honeycomb ising lattices

Progress in the theory of lattice statistics is reviewed with emphasis on the use of series expansions to study the critical behavior and on the exact results obtained by transformation theory. Recent work is reported which indicates that the magnetization of the three‐dimensional Ising model vanishes as (Tc − T)β with β≃516, while the low‐temperature susceptibility diverges as (Tc − T)−γ with γ=54(γ=74 in two dimensions). An Appendix is devoted to a detailed tabulation of the exact numerical values and best estimates for the critical temperatures, energies, specific heats, entropies, magnetizations, and the ferro‐ and antiferromagnetic susceptibilities of four plane lattices and the simple, body‐centered, and face‐centered cubic lattices.A square lattice gas with infinite nearest‐neighbor repulsions and weak second‐neighbor attractions (across alternate squares) is solved exactly for one particular temperature by transformation. The gas undergoes a transition at a density ρt=142, the corresponding form o...

Lattice Statistics‐A Review and an Exact Isotherm for a Plane Lattice Gas

Inhomogeneous differential approximants (J/L;M)f(x), (J/L;M,N)f(x,y) etc. are defined for functions of one or more variables given as power series expansions, and some of their properties are exposed. The approximants are easily computable, and numerical studies are reported (for single-variable series) which demonstrate their utility in circumstances where the customary direct or logarithmic derivative Pade approximants (which are limiting cases) are inadequate.

Michael E. Fisher

Papers

The Yang–Yang relation and the specific heats of propane and carbon dioxide

Magnetic Critical Point Exponents—Their Interrelations and Meaning

Antiferromagnetic susceptibility of the plane square and honeycomb ising lattices

Lattice Statistics‐A Review and an Exact Isotherm for a Plane Lattice Gas

Inhomogeneous differential approximants for power series