Related papers: Universal scaling limits for spin networks via mar…

We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…

This paper extends the Blanket representation of [Universal scaling limits for spin networks via martingale methods, Franchini, S., Proc. R. Soc. A, 481 (2025)] from systems with two-body interactions to multi-spin (or n-body) interactions.…

The finite-size scaling function of the magnetization of the ferromagnetic Heisenberg chain is argued to be universal with respect to the magnitude of the spin. The finite-size scaling function is given explicitly by an analytical…

Consider the mean-field spin models where the Gibbs measure of each configuration depends only on its magnetization. Based on the Stein and Laplace methods, we give a new and short proof for the scaling limit theorems with convergence rate…

Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|{\vec x}|$ to a "trap center", proportionally to $(|{\vec x}|/\ell)^p$, $p>0$. On a…

We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…

We establish the scaling limit of a class of boundary random walks to the full spectrum of Brownian-type processes on the half-line. By solving the associated martingale problem and employing weak convergence techniques, we prove that under…

We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an…

We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of…

We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…

Scale invariance and the resulting power law behaviours are seen in diverse systems. In this work we consider translation, rotational and scale invariant systems defined on a lattice, such that the variables defining the state at every…

We identify the local scaling limit of multiple boundary-to-boundary branches in a uniform spanning tree (UST) as a local multiple SLE(2), i.e., an SLE(2) process weighted by a suitable partition function. By recent results, this also…

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated…

In one dimension very general results from conformal field theory and exact calculations for certain quantum spin systems have established universal scaling properties of the entanglement entropy between two parts of a critical system.…

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…

We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic…

We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These…

We discuss ground state factorization schemes in spin $S$ arrays with general $XYZ$ couplings under general magnetic fields, not necessarily uniform or transverse. It is first shown that given arbitrary spin alignment directions at each…

We derive the distribution of eigenvalues of the reduced density matrix of a block of length l in a one-dimensional system in the scaling regime. The resulting "entanglement spectrum" is described by a universal scaling function depending…

Given a countable set of sites and a collection of flip rates at each site, we give a sufficient condition on the long-range dependancies of the flip rates ensuring the well-definedness of the corresponding spin system. This hypothesis has…