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 …

For statistical mechanical systems with continuous phase transitions, there are two closely
related but subtly different mean-field treatments, the Gaussian fixed point (GFP) in the …

The exact solution of the Ising model on the complete graph (CG) provides an important,
though mean-field, insight for the theory of continuous phase transitions. Besides the …

Besides its original spin representation, the Ising model is known to have the Fortuin-
Kasteleyn (FK) bond and loop representations, of which the former was recently shown to …

We show by extensive simulations that the whole supercritical phase of the three-
dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of …

We consider how finite-size scaling (FSS) is modified above the upper critical dimension,
du= 4, due to hyperscaling violations, which in turn arise from a dangerous irrelevant …

Fractals are ubiquitous in the natural world, and their connection with phase transitions has
been widely observed. This study investigates mechanisms of fractal formation from the …

We investigate $\phi^{2n+ 1} $ deformations of the generalized free theory in the $\epsilon $
expansion, where the canonical kinetic term is generalized to a higher-derivative version …