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

Renormalization-group theory has stood, for over 40 years, as one of the pillars of modern
physics. As such, there should be no remaining doubt regarding its validity. However, finite …

A finite size scaling theory for the partition function zeroes and thermodynamic functions of O
(N) φ4-theory in four dimensions is derived from renormalization group methods. The …

Fisher's fluctuation-response relation is one of four famous scaling formulae and is
consistent with a vanishing correlation-function anomalous dimension above the upper …

The correlation length plays a pivotal role in finite-size scaling and hyperscaling at
continuous phase transitions. Below the upper critical dimension, where the correlation …

It is well known that standard hyperscaling breaks down above the upper critical dimension
d_c, where the critical exponents take on their Landau values. Here we show that this is …

The Finite-Size Scaling Functions of the Four-Dimensional Ising Model Page 1 1397 0022-4715/01/0900-1397$19.50/0
© 2001 Plenum Publishing Corporation Journal of Statistical Physics, Vol. 104, Nos. 5/6 …

The six-dimensional Ising model with nearest-neighbor pair interactions is simulated on the
Creutz cellular automaton by using the finite-size lattices with the linear dimensions L= 4, 6 …

The six-dimensional Ising model is simulated on the Creutz cellular automaton using the
finite-size lattices with the linear dimension 4⩽ L⩽ 12. The exponents in the finite-size …

The spin-1 Ising (BEG) model with the nearest-neighbor bilinear and biquadratic interactions
and single-ion anisotropy is simulated on a cellular automaton which is improved from the …