Related papers: Scaling properties at the interface between differ…
In all local low-dimensional models, scaling at critical points deviates from mean field behavior -- with one possible exception. This exceptional model with ``ordinary" behavior is an inherently non-equilibrium model studied some time ago…
The dependence of the scaling properties of the structure factor on space dimensionality, range of interaction, initial and final conditions, presence or absence of a conservation law is analysed in the framework of the large-N model for…
The phase diagram of a novel two-dimensional frustrated Ising model with both anti-ferromagnetic and ferromagnetic couplings is studied using Tensor-Network Renormalization-Group techniques. This model can be seen as two anti-ferromagnetic…
A cluster Monte Carlo algorithm for the Ashkin-Teller (AT) model is constructed according to the guidelines of a general scheme for such algorithms. Its dynamical behaviour is tested for the square lattice AT model. We perform simulations…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…
We introduce a novel semiclassical approach to the Lipkin model. In this way the well-known phase transition arising at the critical value of the coupling is intuitively understood. New results -- showing for strong couplings the existence…
The Ising model of statistical physics has served as a keystone example of phase transitions, thermodynamic limits, scaling laws, and many other phenomena and mathematical methods. We introduce and explore an Ising game, a variant of the…
The universal critical point ratio $Q$ is exploited to determine positions of the critical Ising transition lines on the phase diagram of the Ashkin-Teller (AT) model on the square lattice. A leading-order expansion of the ratio $Q$ in the…
We prove that the interface separating $+1$ and $-1$ spins in the critical planar Ising model with Dobrushin boundary conditions perturbed by an external magnetic field has a scaling limit. This result holds when the Ising model is defined…
Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
We study the interfaces arising in the two-dimensional Ising model at critical temperature, without magnetic field. We show that in the presence of free boundary conditions between plus and minus spins, the scaling limit of these interfaces…
The Ashkin-Teller (AT) model is a classic spin model in statistical mechanics. For traditional homogeneous lattices like triangular and kagome lattices, even when frustration exists, the model only has one ferromagnetic-paramagnetic…
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical…
First-order phase transitions, classical or quantum, subject to randomness coupled to energy-like variables (bond randomness) can be rounded, resulting in continuous transitions (emergent criticality). We study perhaps the simplest such…
We study the surface critical behavior of semi-infinite quenched random Ising-like systems at the special transition using three dimensional massive field theory up to the two-loop approximation. Besides, we extend up to the next-to leading…
We have performed small-angle light-scattering measurements of the static structure factor of a critical binary mixture undergoing diffusive partial remixing. An uncommon scattering geometry integrates the structure factor over the sample…
We study the ageing properties of the semi-infinite kinetic spherical model at the critical point and in the ordered low-temperature phase, both for Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation ratio and…
The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by…