Критиктік нүктелер физикасы

Physics associated with critical points
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 the physical origin of these phenomena, we shall use the Ising model as a pedagogical example.

The correlation length diverges at the critical point: as , This divergence poses no physical problem. Other physical observables diverge at this point, leading to some confusion at the beginning. The most important is susceptibility. Let us apply a very small magnetic field to the
system in the critical point. A very small magnetic field is not able to magnetize a large coherent cluster, but with these fractal clusters the picture changes. It affects easily the smallest size clusters, since they have a nearly paramagnetic behaviour. But this change, in its turn, affects the next scale clusters, and the perturbation climbs the ladder until the whole system changes radically. Thus, critical systems are very sensitive to small changes in the environment. Other observables, such as the specific heat, may also diverge at this point. All these divergences stem from that of the correlation length.

As we approach the critical point, these diverging observables behave as for some exponent where, typically, the value of the exponent α is the same above and below Tc. These exponents are called critical exponents and are robust observables. Even more, they take the same values for very different physical systems. This intriguing phenomenon, called universality, is explained, qualitatively and also quantitatively, by the renormalization group.

Critical phenomena may also appear for dynamic quantities, not only for static ones. In fact, the divergence of the characteristic time of a system is directly related to the divergence of the thermal correlation length by the introduction of a dynamical exponent z and the relation The voluminous static universality class of a system splits into different, less voluminous dynamic universality classes with different values of z
but a common static critical behaviour, and by approaching the critical point one may observe all kinds of slowing down phenomena. The divergence of relaxation time at criticality leads to singularities in various collective transport quantities, e. g., the interdiffusivity, shear viscosity , and bulk viscosity The dynamic critical exponents follow certain scaling relations, viz., , where d is the space dimension. There is only one independent dynamic critical exponent. Values of these exponents are dictated by several universality classes. According to the Hohenberg−Halperin nomenclature, for the model H universality class (fluids) .

The main mathematical tools to study critical points are renormalization group, which takes advantage of the Russian dolls picture or the self similarity to explain universality and predict numerically the critical exponents, and variational perturbation theory, which converts divergent perturbation expansions into convergent strong coupling expansions relevant to critical phenomena. In two dimensional systems, conformal field theory is a powerful tool which has discovered many new properties of 2D critical systems, employing the fact that scale invariance, along with a few other requisites, leads to an infinite symmetry group.

The critical point is described by a conformal field theory. According to the renormalization group theory, the defining property of criticality is that the characteristic length scale of the structure of the physical system, also known as the correlation length ξ, becomes infinite. This can happen along critical lines in phase space. This effect is the cause of the critical opalescence that can be observed as a binary fluid mixture approaches its liquid–liquid critical point. In systems in equilibrium, the critical point is reached only by precisely tuning a control parameter. However, in some non equilibrium systems, the critical point is an attractor of the dynamics in a manner that is robust with respect to system parameters, a phenomenon referred to as self organized criticality.

Applications arise in physics and chemistry, but also in fields such as sociology. For example, it is natural to describe a system of two political parties by an Ising model. Thereby, at a transition from one majority to the other, the above mentioned critical phenomena may appear.