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Small-world networks provide an interesting framework for studying the interplay between regular and random graphs, where links are located in a regular and random way, respectively. On one hand, the random links make the model to obey some…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3<d<4, with a…
We investigate the effect of quenched surface disorder on effective interactions between two planar surfaces immersed in fluids which are near criticality and belong to the Ising bulk universality class. We consider the case that, in the…
We investigate magnetic properties of the ferromagnetic Ising model on square-triangle tilings to explore how the hyperuniformity, which characterizes long-range behavior of the point pattern, influences critical phenomena where long-range…
We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $ 6 \le L \le 90 $ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each…
We study the critical energy and magnetization profiles for the Ising quantum chain with a marginal extended surface perturbation of the form A/y, y being the distance from the surface (Hilhorst-van Leeuwen model). For weak local couplings,…
We construct an approximate renormalization transformation that combines Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze instabilities in Hamiltonian systems with three degrees of freedom. This scheme is…
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with…
A random-field Ising model that is capable of exhibiting a rich variety of multicritical phenomena, as well as a smearing of such behavior, is investigated. The model consists of an infinite-range-interaction Ising ferromagnet in the…
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…
We propose a novel way of investigating the universal properties of spin systems by coupling them to an ensemble of causal dynamically triangulated lattices, instead of studying them on a fixed regular or random lattice. Somewhat…
The fixed-point structure of three-dimensional bond-disordered Ising models is investigated using the numerical domain-wall renormalization-group method. It is found that, in the +/-J Ising model, there exists a non-trivial fixed point…
The massive field-theory approach for studying critical behavior in fixed space dimensions $d<4$ is extended to systems with surfaces.This enables one to study surface critical behavior directly in dimensions $d<4$ without having to resort…
We address the general problem of hard objects on random lattices, and emphasize the crucial role played by the colorability of the lattices to ensure the existence of a crystallization transition. We first solve explicitly the naive…
The critical behaviour of semi-infinite $d$-dimensional systems with short-range interactions and an O(n) invariant Hamiltonian is investigated at an $m$-axial Lifshitz point with an isotropic wave-vector instability in an $m$-dimensional…
A hyperbolic plane can be modeled by a structure called the enhanced binary tree. We study the ferromagnetic Ising model on top of the enhanced binary tree using the renormalization-group analysis in combination with transfer-matrix…
We calculate the surface critical exponents of the ordinary transition occuring in semi-infinite, quenched dilute Ising-like systems. This is done by applying the field theoretic approach directly in d=3 dimensions up to the two-loop…
We consider the problem associated to recovering the block structure of an Ising model given independent observations on the binary hypercube. This new model, called the Ising blockmodel, is a perturbation of the mean field approximation of…
The Ising model is one of the most well known models in statistical physics, with its critical behavior governed by the Wilson-Fisher universality class (UC). When active motility is incorporated into the Ising model by, e.g., dictating…