This book is the sixth volume of reviews on advanced problems of phase transitions and critical phenomena, with the first five volumes appearing in 2004, 2007, 2012, 2015, and 2018. It aims to provide an overview of those aspects of criticality and related topics that have attracted much attention due to the recent contributions. The six chapters discuss criticality of complex systems, where the new, emergent properties appear via collective behaviour of simple elements. Since all complex systems involve cooperative behaviour between many interconnected components, the field of phase transitions and critical phenomena provides a very natural conceptual and methodological framework for their study. As for the previous volumes, this book is based on the review lectures that were given in Lviv (Ukraine) at the "Ising lectures" — a traditional annual workshop on phase transitions and critical phenomena which aims to bring together scientists working in the field of phase transitions with university students and those who are interested in the topic. The level of presentation makes the book readable both for professionals and the students in the field. On a larger scale, the book may contribute to promoting and deepening studies of phase transitions and critical phenomena. Key Features: o Providing reviews of the state-of-the-art studies in various areas of phase transition theory and related topics that have currently attracted much attention o Focuses on the criticality of complex systems o Presents different aspects of complexity, analyzing systems of non-physical origin and studies the criticality of traditional complex physical objects such as disordered magnets and complex polymers

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