Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2001-07-19
Physics
Condensed Matter
Statistical Mechanics
20 pages; 5 figures
Scientific paper
10.1103/PhysRevB.64.184505
A renormalization-group scheme is developed for the 3-dimensional O($2N$)-symmetric Ginzburg-Landau-Wilson model, which is consistent with the use of a 1/N expansion as a systematic method of approximation. It is motivated by an application to the critical properties of superconductors, reported in a separate paper. Within this scheme, the infrared stable fixed point controlling critical behaviour appears at $z=0$, where $z=\lambda^{-1}$ is the inverse of the quartic coupling constant, and an efficient renormalization procedure consists in the minimal subtraction of ultraviolet divergences at $z=0$. This scheme is implemented at next-to-leading order, and the standard results for critical exponents calculated by other means are recovered. An apparently novel result of this non-perturbative method of approximation is that corrections to scaling (or confluent singularities) do not, as in perturbative analyses, appear as simple power series in the variable $y=zt^{\omega\nu}$. At least in three dimensions, the power series are modified by powers of $\ln y$.
Lawrie Ian D.
Lee Dominic J.
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