Microscopic theory
of the secondorder phase transitions
and critical phenomena


Fine universal structure of the lambdapoint in the dependence of the specific heat capacity on the reduced temperature t = (T — T_{c})/Т_{с} in the critical region of the BoseEinstein condensation for a mesoscopic trap with an ideal gas 

Despite the applied orientation of the Institute, great attention in its work is given to the solution of the fundamental problems in the theoretical physics. Recently, the longstanding problem of finding the microscopic theory and universal mechanism of the secondorder phase transitions has been solved. The basics of the nonperturbation microscopic theory of the spontaneous symmetry breaking and related critical phenomena have also been formulated. The theory is based on the explicit isolation of the universal constraint nonlinearity (interaction), which is determined by the breaking symmetry and originates due to restraining the manybody Hilbert space by the integrals of motion (constraints) in accordance with the Noether theorem. That constraintcutoff mechanism is responsible for the phase transition to the state with the BoseEinstein condensate even in an ideal gas, i.e., in the absence of the interparticle interaction
(V. V. Kocharovsky, Vl. V. Kocharovsky).
The universal probability distribution of the number of particles in the BoseEinstein condensate of an ideal gas in a mesoscopic trap with arbitrary temperature, volume, and particle number has been found and described by the exact analytical formula for the first time. All universality classes and a remarkable selfsimilarity of the statistics and thermodynamics of the BoseEinstein condensed ideal gas in different mesoscopic traps have been found. In particular, a universal critical behavior of the specific heat capacity in the critical region, i.e., a universal structure of the lambda point, has been found analytically for an ideal gas in a mesoscopic trap. It has been shown that the obtained universal formulas for the order parameter and all higher moments of the condensate fluctuations match the known asymptotics on both sides of the critical region (the Landau meanfield theory) and agree with the specific results of the phenomenological renormalizationgroup theory, which is valid in the narrow central part of the critical region.