129 citations · 1.6k across the 77 of their papers we have counts for
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Scaling and Finite-Size Scaling above the Upper Critical Dimension
Ralph Kenna, Bertrand Berche
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of s…
The fifty-year quest for universality in percolation theory in high dimensions
T. Ellis, R. Kenna, B. Berche
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the effic…
Potts Model with Invisible States: A Review
Mariana Krasnytska, Petro Sarkanych, Bertrand Berche +2
The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems whe…
Phase transitions above the upper critical dimension
Bertrand Berche, Tim Ellis, Yurij Holovatch +1
These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension …
Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
Mariana Krasnytska, Bertrand Berche, Yurij Holovatch +1
We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising…
Universality and exact finite-size corrections for spanning trees on cobweb and fan networks
Nickolay Izmailian, Ralph Kenna
Universality is a cornerstone of theories of critical phenomena. It is well understood in most systems especially in the thermodynamic limit. Finite-size systems present additional…