These lecture notes provide an overview of the renormalization group (RG) as a successful
framework to understand critical phenomena above the upper critical dimension $ d_ {\rm …

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 …

Above the upper critical dimension, the breakdown of hyperscaling is associated with
dangerous irrelevant variables in the renormalization group formalism at least for systems …

We investigate the location of the critical and tricritical points of the three-dimensional Blume-
Capel model by analyzing the behavior of the first Lee-Yang zero, the density of partition …

Using the electrostatic analogy, we derive an exact formula for the limiting Yang-Lee zero
distribution in the random allocation model of general weights. This exhibits a real-space …

Multiplicative logarithmic corrections frequently characterize critical behavior in statistical
physics. Here, a recently proposed theory relating the exponents of such terms is extended …

Field-theoretical calculations predict that, at the upper critical dimension dc= 4, the finite-size
scaling (FSS) behaviors of the Ising model would be modified by multiplicative logarithmic …

This chapter starts with an overview of Monte Carlo computer simulation methodologies
which are illustrated for the simple case of the Ising model. After reviewing importance …

The very existence of a phase transition for spin glasses in an external magnetic field is
controversial, even in high dimensions. We carry out massive simulations of the Ising spin …

The effects of bond randomness on the universality aspects of a two-dimensional (d= 2)
Blume-Capel model embedded in the triangular lattice are discussed. The system is studied …