Research interests
My current research interests are centered upon phase transitions and critical behaviour. As far as critical behaviour is almost always accompanied by appearance of universal scaling (power) laws, the models used for its description and the methods applied allow for conceptual understanding and interpretation of a wide range of phenomena in various systems, not necessarily of physical origin. In particular, I am interested in qualitative understanding and accurate quantitative description of criticality and scaling in complex systems. The notion of a complex system is currently understood by a physical community as either a system who's behaviour crucially depends on the details of the system or as a systems of many interacting entities of non-physical origin. In my research I dealt with complexity in both above mentioned senses. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena gives a very natural conceptual and methodological framework for their study. Our methods include both analytical approaches (field theoretical renormalization group, functional integration, resummation of divergent series,
phenomenological thermodynamical approach), numerical simulations, and empirical data analysis. Particular problems, I and my collaborators studied recently concern domains of magnets, polymers, and complex networks. I describe them briefly below, referring to our review or representative research papers.
Polymers
Magnets
Complex networks