aqora

Absence of hyperscaling violations for phase transitions with positive specific heat exponent

Rudolf Hilfer A

The European Physical Journal BMar 1, 199426 citations

Violations of Hyperscaling in Phase Transitions and Critical Phenomena

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.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.

MDPI eBooksSep 24, 20250 citations

Ralph Kenna’s Scaling Relations in Critical Phenomena

Leïla Moueddene, Arnaldo Donoso, Bertrand Berche

In this note, we revisit the scaling relations among "hatted critical exponents", which were first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an alternative derivation for some of them. For the scaling relation involving the behavior of the correlation function, we will propose an alternative form since we believe that the expression is erroneous in the work of Ralph and his collaborators.

arXiv:2402.00427EntropyFeb 29, 20248 citations

Recent developments in phase transitions and critical phenomena

David R. Nelson

NatureSep 1, 197719 citations

Overview of phase transitions and critical phenomena

Mário J. de Oliveira

AbstractJan 1, 20060 citations

Order, Disorder and Criticality - Advanced Problems of Phase Transition Theory Volume 2

Ergodicity Violation and Ageing in Anomalous Diffusion (Ralf Metzler) Microscopic Approach to the Kinetics of Pattern Formation (Helene Zapolsky) Scaling above the Upper Critical (Bertrand Berche & Ralph Kenna) Simplexity of Geometrically Frustrated Ising Antiferromagnets (Taras Yavorskii) Monte Carlo Simulation of Critical Casimir Forces (Oleg A Vasilyev) From Real Space Renormalization Group to the Making of Public Opinion: An Approach from Sociophysics (Serge Galam)

WORLD SCIENTIFIC eBooksJan 1, 200722 citations

Violations of Hyperscaling in Phase Transitions and Critical Phenomena—In Memory of Prof. Ralph Kenna

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Violations of Hyperscaling in Phase Transitions and Critical Phenomena—In Memory of Prof. Ralph Kenna

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