Journal of Physical Studies 1(3), 343–355 (1997) DOI: https://doi.org/10.30970/jps.01.343 IS THE NORMAL-TO-SUPERCONDUCTING TRANSITION OF FIRST OR SECOND ORDER?

R. Folk^*, Yu. Holovatch^**
*Institut für Theoretische Physik, Johannes Kepler Universität Linz, A-4040 Linz, Austria
^**Institute for Condensed Matter Physics of the Ukrainian Acad. Sci. 1 Svientsitskii Str., Lviv UA-290011, Ukraine

We study the phase transition to the superconducting state taking into account the fluctuations of the order parameter and of the vector magnetic field and discuss the question of the order of transition occuring in this model. We use the filed–theoretical renormalization group approach and consider the field–theoretical gauge model for a superconductor, generalized to a $n/2$ component complex order parameter. Renormalization group calculations within strict $ε$-expansion suggested that in such a model a first-order phase transition occurs. We re-examine the previously obtained expressions for the renormalization group functions in a two-loop approximation in three dimensions. Special attention is being payed to the fact, that the corresponding series might be asymptotic ones and therefore have zero radius of convergence. We discuss possible ways of the analytical continuation of the series obtained. On the basis of the comparison of the results obtained by ‟direct" calculations with those obtained by Padé analysis and Padé–Borel resummation technique the conjecture is made that in the model under consideration still exists a possibility for the second-order phase transition with the critical exponents differing from those of a superfluid liquid. This is in agreement with conclusions made very recently in other nonperturbative treatments.

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