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Tricritical Point
In condensed matter physics, dealing with the macroscopic physical properties of matter, a tricritical point is a point in the phase diagram of a system at which three-phase coexistence terminates. This definition is clearly parallel to the definition of an ordinary critical point as the point at which two-phase coexistence terminates. A point of three-phase coexistence is termed a triple point for a one-component system, since, from Gibbs' phase rule, this condition is only achieved for a single point in the phase diagram (''F'' = 2-3+1 =0). For tricritical points to be observed, one needs a mixture with more components. It can be shown that three is the ''minimum'' number of components for which these points can appear. In this case, one may have a two-dimensional region of three-phase coexistence (''F'' = 2-3+3 =2) (thus, each point in this region corresponds to a triple point). This region will terminate in two critical lines of two-phase coexistence; these two critical lines ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the subject deals with "condensed" phases of matter: systems of many constituents with strong interactions between them. More exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, and the Bose–Einstein condensate found in ultracold atomic systems. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theories to develop mathematical models. The diversity of systems and phenomena available for study makes condensed matter phy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kagome Lattice
In geometry, the trihexagonal tiling is one of 11 uniform tilings of the Euclidean plane by regular polygons. See in particular Theorem 2.1.3, p. 59 (classification of uniform tilings); Figure 2.1.5, p.63 (illustration of this tiling), Theorem 2.9.1, p. 103 (classification of colored tilings), Figure 2.9.2, p. 105 (illustration of colored tilings), Figure 2.5.3(d), p. 83 (topologically equivalent star tiling), and Exercise 4.1.3, p. 171 (topological equivalence of trihexagonal and two-triangle tilings). It consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. The name derives from the fact that it combines a regular hexagonal tiling and a regular triangular tiling. Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines. Its dual is the rhombille tiling. This pattern, and its place in the classification of uniform tilings, was already known to Johann ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of ris ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ginzburg–Landau Theory
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. One GL-type superconductor is the famous YBCO, and generally all Cuprates. Later, a version of Ginzburg–Landau theory was derived from the Bardeen–Cooper–Schrieffer microscopic theory by Lev Gor'kov, thus showing that it also appears in some limit of microscopic theory and giving microscopic interpretation of all its parameters. The theory can also be given a general geometric setting, placing it in the context of Riemannian geometry, where in many cases exact solutions can be given. This general setting then extends to quantum field theory and string theory, again owing to its solvability, and its close relation to other, simi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type II Superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the formation of magnetic field vortices with an applied external magnetic field. This occurs above a certain critical field strength ''Hc1''. The vortex density increases with increasing field strength. At a higher critical field ''Hc2'', superconductivity is destroyed. Type-II superconductors do not exhibit a complete Meissner effect. History In 1935, Rjabinin and Shubnikov experimentally discovered the Type-II superconductors. In 1950, the theory of the two types of superconductors was further developed by Lev Landau and Vitaly Ginzburg in their paper on Ginzburg–Landau theory. In their argument, a type-I superconductor had positive free energy of the superconductor-normal metal boundary. Ginzburg and Landau pointed out the possibilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I Superconductor
The interior of a bulk superconductor cannot be penetrated by a weak magnetic field, a phenomenon known as the Meissner effect. When the applied magnetic field becomes too large, superconductivity breaks down. Superconductors can be divided into two types according to how this breakdown occurs. In type-I superconductors, superconductivity is abruptly destroyed via a first order phase transition when the strength of the applied field rises above a critical value ''H''c. This type of superconductivity is normally exhibited by pure metals, e.g. aluminium, lead, and mercury. The only alloy known up to now which exhibits type I superconductivity is TaSi2. The covalent superconductor SiC:B, silicon carbide heavily doped with boron, is also type-I. Depending on the demagnetization factor, one may obtain an intermediate state. This state, first described by Lev Landau, is a phase separation into macroscopic non-superconducting and superconducting domains forming a Husimi Q representation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is professor of theoretical physics at the Free University of Berlin, Germany (since 1968)Honorary Doctorat the West University of Timișoaraandat thin Bishkek. He is alsHonorary Memberof th For his contributions to particle and solid state physics he wathe Max Born Prize 2008 witMedal His contribution to thmemorial volumecelebrating the 100th birthday of Lev Davidovich Landau earned him the Majorana Prize 2008 with Medal. He is married to Dr. Annemarie Kleinert since 1974 with whom he has a soMichael Kleinert Publications Kleinert has written ~420 papers on mathematical physics and the physics of elementary particles, nuclei, solid state systems, liquid crystals, biomembranes, microemulsions, polymers, and the theory of financial markets. He has written several books on theoretical physics, the most notable of which, ''Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets,'' has been published in five edition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superconduction
Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source. The superconductivity phenomenon was discovered in 1911 by Dutch physicist Heike Kamerlingh Onnes. Like ferromagnetism and atomic spectral lines, superconductivity is a phenomenon which can only be explained by quantum mechanics. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor during its transitions into the super ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Landau Theory
Landau theory in physics is a theory that Lev Landau introduced in an attempt to formulate a general theory of continuous (i.e., second-order) phase transitions. It can also be adapted to systems under externally-applied fields, and used as a quantitative model for discontinuous (i.e., first-order) transitions. Although the theory has now been superseded by the renormalization group and scaling theory formulations, it remains an exceptionally broad and powerful framework for phase transitions, and the associated concept of the Phase transitions#Order parameters, order parameter as a descriptor of the essential character of the transition has proven transformative. Mean-field formulation (no long-range correlation) Landau was motivated to suggest that the free energy of any system should obey two conditions: *Be analytic in the order parameter and its gradients. *Obey the symmetry of the Hamiltonian mechanics, Hamiltonian. Given these two conditions, one can write down (in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous states) occur and coexist at equilibrium. Overview Common components of a phase diagram are ''lines of equilibrium'' or ''phase boundaries'', which refer to lines that mark conditions under which multiple phases can coexist at equilibrium. Phase transitions occur along lines of equilibrium. Metastable phases are not shown in phase diagrams as, despite their common occurrence, they are not equilibrium phases. Triple points are points on phase diagrams where lines of equilibrium intersect. Triple points mark conditions at which three different phases can coexist. For example, the water phase diagram has a triple point corresponding to the single temperature and pressure at which solid, liquid, and gaseous water can coexist in a stabl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Dimension
In the renormalization group analysis of phase transitions in physics, a critical dimension is the dimensionality of space at which the character of the phase transition changes. Below the lower critical dimension there is no phase transition. Above the upper critical dimension the critical exponents of the theory become the same as that in mean field theory. An elegant criterion to obtain the critical dimension within mean field theory is due to V. Ginzburg. Since the renormalization group sets up a relation between a phase transition and a quantum field theory, this has implications for the latter and for our larger understanding of renormalization in general. Above the upper critical dimension, the quantum field theory which belongs to the model of the phase transition is a free field theory. Below the lower critical dimension, there is no field theory corresponding to the model. In the context of string theory the meaning is more restricted: the ''critical dimension'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Behavior
In physics, critical phenomena is the collective name associated with the physics of critical points. Most of them stem from the divergence of the correlation length, but also the dynamics slows down. Critical phenomena include scaling relations among different quantities, power-law divergences of some quantities (such as the magnetic susceptibility in the ferromagnetic phase transition) described by critical exponents, universality, fractal behaviour, and ergodicity breaking. Critical phenomena take place in second order phase transitions, although not exclusively. The critical behavior is usually different from the mean-field approximation which is valid away from the phase transition, since the latter neglects correlations, which become increasingly important as the system approaches the critical point where the correlation length diverges. Many properties of the critical behavior of a system can be derived in the framework of the renormalization group. In order to explain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
