Fluctuations in the Lattice Ginzburg-Landau Model

Abstract

Fluctuations in type-II superconductors near the upper crytical magnetic field H _c2 (T) have been studied for many years [1] -[9]. Attempts to develop a consistent theory encounter serious difficulties. The dimentions reduction d → d — 2 due to the background field makes fluctuations to be more important for the thermodynamics. Fluctuation correction to t he specific heat, e.g. takes the form

$$ \Delta C(\tau ) = \int {{d^{d - 2}}q\frac{1}{{{{({q^2} + \tau )}^2}}}} \sim {\tau ^{ - (6 - d)/2}} $$

(1)

where τ ∼ (T — T _C )/T _C . Thus one can see that this correction can essentials influence the crytical behaviour and, in particular. the phase transition order. What is more, this means that a continuous phase transition cannot occur in such a system because the lower crytical dimention equals four [7]. [8]. In this paper we give a brief review of the works carried out by our group and dedicated to an investigation of this problem.