A one-step real-space renormalization group (RSRG) transformation is used to study the q-state Potts model on the two-dimensional (2D) Penrose tiling (PT). The critical exponents of the correlation length ν(q) in the region between q=1 and q=4 are obtained. The bond percolation (BP) threshold...

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Three examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated...

A new position-space renormalization group approach is investigated for bond directed percolation in two dimensions. The threshold value for the bond occupation probabilities is found to be pc=0.6443. Correlation length exponents on time (parallel) and space (transverse) directions are found to...

The directed Abelian sandpile models are defined on a square lattice by introducing a parameter, c, representing the degree of anisotropy in the avalanche processes, in which c=1 is for the isotropic case. We calculate the expected number of the topplings per added particle, 〈T〉, which...

The light scattering measurements that yield the osmotic susceptibility (χT) in a ternary liquid mixture of 3-methylpyridine+water+sodiumbromide are presented. The measurements have been performed in the one-phase region near the lower consolute points TL's of samples with different...

The phase diagram of an asymmetric N=3 Ashkin–Teller model is obtained by a numerical analysis which combines Monte Carlo renormalization group and reweighting techniques. Present results reveal several differences with those obtained by mean-field calculations and a Hamiltonian approach. In...

We re-examine a population model which exhibits a continuous absorbing phase transition belonging to directed percolation in 1D and a first-order transition in 2D and above. Studying the model on Sierpinski Carpets of varying fractal dimensions, we examine at what fractal dimension 1≤df≤2,...

We study the critical behavior of surface-interacting self-avoiding random walks on a class of truncated simplex lattices, which can be labeled by an integer n ⩾ 3. Using the exact renormalization group method we have been able to obtain the exact values of various critical exponents for all...

The critical properties of short-range Ising spin-glass models, defined on diamond hierarchical lattices of graph fractal dimensions df=2.58,3, and 4, and scaling factor 2, are studied via a method based on the Migdal–Kadanoff renormalization-group scheme. The order-parameter critical exponent...

The role of the distribution of coupling constants in the critical exponents of the short-range Ising spin-glass model is investigated via real space renormalization group. A saddle-point spin glass critical point characterized by a fixed-point distribution is found in an appropriated parameter...