Order and disorder in nature has been among the key questions throughout the human history. Essentially all substances in nature that we experience through our sensory organs are many-particle systems consisting of a large number of constituent particles, say, atoms or molecules. Such macroscopic systems may display either disorder or order, depending on the relative strength of random fluctuations and cooperativity (via interactions) among constituents.
Often many generic systems in nature behave neither in the fully ordered nor in the completely disordered manner, exhibiting complexity. Although there does not exist a precise definition of complexity (otherwise the system is perhaps no longer "complex"), it is usually characterized by large variability. Such complexity is observed in extended dissipative dynamical systems having many (meta)stable states. The key ingredients for such complicated energy landscape consisting of many valleys and barriers of various sizes are frustration due to competing interactions and quenched randomness. In addition the environment may also play an important role, supplying information, driving, fluctuations, and so on. Complex systems, possessing these ingredients, are generic and ubiquitous in nature; diverse complex phenomena are displayed by a variety of complex systems in physics, biology, and social sciences, and understanding them offers a challenge in this century. A potpourri of popular complex systems includes glasses, granular assembly or powder, coupled-oscillator systems, biological systems, traffic flow, optimization problems, complex networks, and socio-economic systems.
Our group is devoted to researches in emergence and complexity. We have been studying physics (or theoretical science) of complex systems, which include biological and social systems as well as conventional matter. In spite of the extreme variety, the complex systems have some general features associated with large variability arising from frustration and/or randomness. In particular they are rather insensitive to the details of the model, not depending on the specific form of, e.g., interactions. Although the precise dynamics of a complex system is usually far beyond our present knowledge, such "universality" gives support to the use of simple models for the complex systems in the real world, and suggests that the idea of information-exchange dynamics, which attempts to provide a framework to describe the ubiquity of criticality, indeed gives a plausible mechanism for complexity in nature.
It should be stressed that collective properties as characteristics of the whole complex system play key roles in most of interesting phenomena in nature. Such properties may not be reduced to the properties of individual constituent particles; they emerge as a result of the cooperative phenomena between constituent particles. These notions of complex systems apparently suggest us to shift the dominant paradigm in physics, from reductionism and determinism to holism and unpredictability.