This special issue of Journal of Physics A: Mathematical and General is a
collection of articles dealing with the application of renormalization
group methods to a wide range of problems in physics. Most articles
are based on contributions presented at the 6th International
Conference, Renormalization Group 2005 (RG 2005), held at the
University of Helsinki from 30 August to 3--September 2005. This was
the sixth of a series of conferences on this topic, the first three
of which took place in 1986, 1991 and 1996 at the Joint Institute for
Nuclear Research in Dubna, Russia. The fourth (RG99) was held in 1999 in
Taxco, Mexico, and the fifth (RG02) in 2002 in Tatranska Strba,
Slovakia.
During the second half of the 20th century a number of important and
very successful new paradigms such as scale-dependent (`running')
coupling constants, scaling, and universality became firmly
established in physics. To a large extent, these advances were due to
the development of renormalization group ideas and their successful
implementation as powerful calculational schemes to tackle problems
with many length scales. While the concept of the renormalization
group had originally been introduced in elementary particle physics,
its modern form eventually emerged from the study of problems in
condensed matter physics, such as critical phenomena and the Kondo
effect. This in turn has significantly reshaped our understanding of
field theories in high energy physics, and produced powerful
computational tools for dealing with difficult many-length-scale
problems in distinct fields of physics, ranging from elementary particle and
condensed matter physics to hydrodynamic turbulence and growth
phenomena in nonequilibrium physics. The history of the
renormalization group, characterized by frequent exchanges of ideas
between elementary particle and condensed matter physics, bears
testimony to the enormous benefits to which such exchanges can lead.
The main aim of the series of renormalization group conferences has
been to bring together scientists with backgrounds and expertise in
the application of the renormalization group to problems in broadly
different areas of physics, offering regular events for continuing
such fruiful exchanges of ideas. We hope that the present collection
of contributions to quantum field theory, mathematical and
methodological aspects of the renormalization group, statistical
mechanics, condensed matter physics, and stochastic dynamics conveys
this spirit. We feel it amply demonstrates the breadth of
activity of research based on the renormalization group and its
potential for future work.
On behalf of the organizers of the conference, we would like to
thank the sixty participants of the conference and the members of the
Advisory Board for their contributions. Financial and
organizational support of the University of Helsinki, the Academy
of Finland, the Finnish Society of Sciences and Letters and the
Naval Academy is gratefully acknowledged. We are very grateful to
all authors who contributed to this special issue. Finally, we owe
special thanks to all who assisted in the preparation of it, in
particular to the staff of Journal of Physics A:
Mathematical and General.