MULTICRITICAL POINTS

1. CRITICAL DIMENSIONS OF STRONGLY INTERACTING ANISOTROPIC SYSTEMSBabich ArtemInstitute of Electrophysics and Radiation Technologies NAS of Ukraine

2. Conception of physical space dimension was immutable for a long period of time. The question about a number of dimensions was rather philosophic problem than problem of natural science. The progress of physic in XX century changed this picture. One of the most important steps on this way was the invention of general relativity. The clear “picture” of 3-dimensional Euclidian space and 1-dimensional time changed to the 4-dimensional riemannian space-time. Further progress of physics, especially in such fields as particle physics and cosmology, has put many questions about dimensionality of the space. Does dimensionality of space equal 3? Is it a constant value? The spaces of various type of M-theory, the spaces of various types of early universe cosmology etc. are the some of examples of spaces of various dimensions.

3. Other example of changing of the conception of the space dimension one can see in the theory of critical phenomena.In modern theory of critical phenomena the space dimensionality is usually considered as continuous value. It appears in thermodynamic relations as one of the model parameters. • One of the most important steps in the investigation of PT was creating of the Landau theory of phase transitions. It allows to describe different kinds of PT using similar methods based on the conception of spontaneous symmetry breaking and mean field approximation. But quantitative predictions of the Landau theory didn’t coincide neither with experimental data nor with numerical calculations. The reason was clear: mean field approximations wasn’t valid in a vicinity of a critical point (point of phase transitions)

4. Next step was the creation of the fluctuation theory of PT. It is based on the renorm group transformation. It allowed to improve quantitative results. But it is much more complicated than Landau theory. Therefore it was important to find an area of applicability of the Landau theory. In the vicinity of points of PT the influence of physical values fluctuations is very intense. The influence of fluctuations strongly depends on space dimension. One of the effects of this dependence is an existence of the 2 critical (or borderline) dimensions: lower and upper.

9. MULTICRITICAL POINTS • In order to describe PT in multicritical point one has to take into account terms with higher nonlinearities of OP. Multicritical point separates first and second order phase transitions. Phase diagram of system with tricritical point

10. Other example of more complicated systems is a system with Lifshitz point. Originally the conception of the Lifshitz point was introduced to describe the phase transition in systems with anisotropic magnetic properties. But recently it has been often used in the theory of black halls, quantum gravity(Horava-Lifshitz gravity) and cosmology.

13. For example tricritical Lifshitz point was investigated in some ferroelectrics (Sn2P2(SexS1–x)6) Phase diagram of Sn2P2(SexS1–x)6 (Yu.M. Vysochansky. V.Yu. Slivka)

24. We proposed the new model that describes PT in multidimensional anisotropic system with higher OP nonlinearities and found CDs of this model. • Next step: calculating of critical indexes. But in general case it is may be very difficult or even impossible. • Searching for possible candidates: Multidimensional anisotropic field theories; Anisotropic cosmologic models.

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