Alexander E. Filippov

Fluctuation effects in an exactly solvable model of phase transitions

Abstract An investigation is made of an exactly solvable phase transition model, which takes account of interaction only between fluctuations with equal and antiparallel momenta. It is shown that within this model fluctuation-induced first-order phase transitions are possible in agreement with renormalization group analysis predictions. The model is generalized phenomenologically, which leads to correct values of all large critical exponents. The effect of frozen-in impurities on a phase transition is studied and it is shown that in a narrow range proportional to the impurity concentration the phase transition smears.

New small RG parameter

Abstract The exact functional renormalization group (RG) equation is used to construct a new version of the perturbation theory whose small parameter is the Fisher exponent η.

Critical behavior and finite volume

An exactly solvable model is used to investigate the influence of the finite size of a system on its critical behavior. The renormalization of the critical temperature is calculated together with the critical exponents and the correlation function. A crossover of the critical exponents from their scaling values to the exponents of mean field theory is obtained. The possibility of complete disappearance of the region of scaling under the influence of the finite size of the system is demonstrated.

Nucleation at the fluctuation induced first order phase transition to superconductivity

Abstract The kinetics of fluctuations arising from vortex pairs in a superconductor at the phase transition from the paraphase to the ordered state is studied. It is shown by numerical simulations that these pairs are generated by typical configurations of the two-component order parameter due to its interaction with a (gauge) electromagnetic field. The role of these excitations in the first order phase transition is discussed.

Oxygen ordering at the structural phase transition in Y-Ba-Cu-O

Abstract A model of the structural phase transition in the high-T c superconducting compound YBa2Cu3O x is proposed which takes into account oxygen atom redistribution in the basal plane and the interaction of oxygen atoms with each other and with oxygen vacancies. The model allows one to obtain the exact partition function and to determine the temperature dependence of the oxygen atom concentration which qualitatively agrees with that observed experimentally.

The RG method applied to an exactly solvable model of phase transitions

The renormalisation group (RG) method is applied to the investigation of an exactly solvable phase transition model in which only the interaction between fluctuations with equal and antiparallel momenta is taken into account. The RG equation for the model is derived, its exact solution and critical asymptotics are obtained. It is shown that direct calculation of the partition function and solution of the RG equation for the model lead to identical results.

The scale equations in the critical dynamics of fluctuating systems

The scale equation method is applied to the investigation of the critical dynamics of systems described by Ginzburg-Landau functionals of the most general form. The method does not require renormalizability of the Ginzburg-Landau functional and does not make use of the scaling invariance hypothesis.

Nonlinear Excitations in the Critical Region

The free energy transformation due to fluctuations is investigated in an exactly solvable model. This model accounts for the fluctuation interaction in a reduced manner and leads to a realistic estimation for the free energy. In particular it gives a nice critical exponentδ=5. It is shown that in spite of the monotonic character of the effective free energy in the critical region the properties of the system should be described on the basis of theϕ6 model. Localized nonlinear excitations are found to be possible with a profile rather like that known as a “bump” near the point of the first-order phase transition.

Fluctuation-induced phase transition of the first kind in an exactly solvable model

A system with cubic anisotropy of the vertices of fourth order is investigated in the framework of a model that admits exact calculation of the partition function. It is shown that for a definite relationship between the parameters of the free energy functional the phase transition in such a system becomes abrupt, whereas mean field theory predicts a phase transition of the second kind under the same conditions. The result agrees with the analogous predictions of fluctuation theory.

Critical behaviour of orthorhombic high Tc superconducting systems with d-pairing

Abstract The prediction of possible superconductivity transition splitting in orthorhombic high T c superconducting systems based on the Landau theory is tested by the renormalization group technique. It is shown that at small orthorhombicity Δ this splitting is absent and appears only at some Δ min .