This special issue of the CMP is devoted to phase transitions and critical phenomena. Several recent decades of intensive, sometimes even frantic, and fruitful activities might produce an impression that all principal work in this field has already been completed and nothing really new can be found. Of course, this is far from being true, and the aim of the present issue is to give an evidence that the field is still fertile and thankful to those who work hard on it. We hope that the readers will find this evidence in the presented papers for which we cordially thank their authors who share this aim of ours and our devotion to the subject. \n \nA specially pleasant mission of this issue is to pay tribute to our distinguished colleague and friend Mykhailo Kozlovskii, member of the CMP Editorial Board, who has been working in the theory of phase transitions for nearly 40 years. In August 2012, Mykhailo crossed a magic line of time, called a sixty years jubilee, and thus reached the age of maturity and wisdom. With this regard, we wish him good health and many years of fruitful and joyful life among his favorite collective variables, fishing, invariably beloved family, and faithful friends. We also wish him to open new horizons and to explore further bystreets in statistical physics, to meet new friends, colleagues and followers.
This special issue of the CMP is devoted to phase transitions and critical phenomena. Several recent decades of intensive, sometimes even frantic, and fruitful activities might produce an impression that all principal work in this field has already been completed and nothing really new can be found. Of course, this is far from being true, and the aim of the present issue is to give an evidence that the field is still fertile and thankful to those who work hard on it. We hope that the readers will find this evidence in the presented papers for which we cordially thank their authors who share this aim of ours and our devotion to the subject. \n \nA specially pleasant mission of this issue is to pay tribute to our distinguished colleague and friend Mykhailo Kozlovskii, member of the CMP Editorial Board, who has been working in the theory of phase transitions for nearly 40 years. In August 2012, Mykhailo crossed a magic line of time, called a sixty years jubilee, and thus reached the age of maturity and wisdom. With this regard, we wish him good health and many years of fruitful and joyful life among his favorite collective variables, fishing, invariably beloved family, and faithful friends. We also wish him to open new horizons and to explore further bystreets in statistical physics, to meet new friends, colleagues and followers.
This Special Issue was initiated by Prof. Ralph Kenna (August 27, 1964October 26, 2023), who, at the time, was a member of the Entropy Editorial Board and it is dedicated to his memory. Universality is a striking feature of critical phenomena, and its origin is largely illuminated by the renormalization group. Universality allows for the essential aspects of critical behaviour in complex physical systems to be captured through highly simplified models, where only key components such as spatial dimensionality, symmetry, and interaction range are retained. Both theoretical models and real systems are thus grouped into universality classes, which are characterised by sets of critical exponents connected through scaling relations. When these relations explicitly involve dimensionality, they are referred to as hyperscaling.In many systems with a high degree of connectivity, mean-field theory provides accurate predictions independently of spatial dimension, leading to the common assertion that hyperscaling breaks down in such cases. However, this conventional view has been reconsidered in light of recent renormalization group developments, which suggest mechanisms by which hyperscaling might be preserved in an extended version even above the upper critical dimension. The contributions collected in this reprint address these issues, focusing on scaling properties beyond the upper critical dimensionality as well as related challenges in the broader theory of phase transitions and critical phenomena.
Abstract Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.
This book is the third volume of review papers on advanced problems of phase transitions and critical phenomena, following the success of the first two volumes in 2004 and in 2007. Broadly, the book aims to demonstrate that the phase transition theory, which experienced its 'golden age' during the 70s and 80s, is far from over and there is still a good deal of work to be done, both at the fundamental level and in respect of applications. This volume presents a broad spectrum of problems connected with criticality. It covers its theoretical backgrounds, analytical approaches and numerical simulations to describe criticality in specific systems (ionic fluids, diluted magnets, polymers), as well as phase transitions on complex networks and in the minority game model. As the first two 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 brings together scientists working in the field with university students and those who are interested in the subject.
Abstract The approaches described so far in this book have given a broad phenomenological understanding of critical phenomena. However, although a substantial framework of results and connections has been built up, we have, as yet, no explanations for the following: What is needed is a theory, based on the physics of what is happening at the critical point. we argued in Chapter 1 that the special feature of criticality is that the correlation length is infinite and that the critical system is invariant on all length scales. The aim is to write down a (hopefully short, elegant, and comprehensible) mathematical theory which embodies this physics and explains all the observations listed above. A useful theory will also allow the calculation of critical exponents and transition temperatures, if not exactly, then within an accurate and well-controlled approximation scheme.
Fluctuations and criticality (dedicated to Reinhard Folk on his 60th birthday)It is our pleasure and honour to present a collection of papers dedicated to Reinhard Folk on the occasion of his 60th birthday.With this Festschrift, colleagues and friends of the jubilee pay tribute to his long lasting and fruitful work in the field of condensed matter physics.His research includes ferroelectric and ferromagnetic phase transitions in regular and disordered systems, neural networks, superconductivity, critical dynamics -this list can be continued.Those, who work in the above mentioned fields certainly know and often use results obtained by R.F. which are currently turning into scientific Folk-lore.However, those who know him personally, recognizing his important contribution to physics, enjoy marvelous features of his extraordinary personality.Openness, readiness for discussion, erudition, interest in people and concern in their problems, sense of humour -that's what makes communication with him so desirable and pleasant.Moreover, his vivid interest in science on a larger scale and a deep concern in its future lead R.F. to activities in science organizations in Austria and the European Union, to his personal participation in different projects aiming at strengthening collaboration with Central and Eastern European countries.His work in this respect is widely recognized and acknowledged by the scientific community.Dear Reinhard, may your work in future lead you to new discoveries and solutions of puzzles put to us almost on every step of research, may it give you satisfaction of the achieved results, and may we, your friends, enjoy for many more years the wonderful intellectual atmosphere created by your work and your spirit.