相关论文: Reply to the Comment on``Scaling Laws for a System…
We progress finite-size scaling in systems with free boundary conditions above their upper critical dimension, where in the thermodynamic limit critical scaling is described by mean-field theory. Recent works show that the correlation…
Systems with long-range interactions often exhibit power-law distributions and can by described by the non-extensive statistical mechanics framework proposed by Tsallis. In this contribution we consider a simple model reproducing continuous…
The thermodynamic and dynamical properties of an Ising model with both short range and long range, mean field like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically…
New methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions. Generically, such systems have entropies which are non-extensive, (do not scale with the size of the system). We show how to…
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…
The quantum long-range extended Ising model possesses several striking features that cannot be observed in the corresponding short-range model. We report that the pattern obtained from the entanglement between any two arbitrary sites of the…
We extend Araki's well-known results on the equivalence of the KMS condition and the variational principle for equilibrium states of quantum lattice systems with short-range interactions, to a large class of models possibly containing…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
Obtaining quantitative ground-state behavior for geometrically-frustrated quantum magnets with long-range interactions is challenging for numerical methods. Here, we demonstrate that the ground states of these systems on two-dimensional…
A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin…
The Lieb-Schultz-Mattis (LSM) theorem asserts that microscopic details of the system can impose non-trivial constraints on the system's low-energy properties. While traditionally applied to short-range interaction systems, where locality…
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…
In Statistical Mechanics, Tsallis distributions were apparently conceived in connection with systems presenting long--range interactions. In fact, they were observed in numerical computations for models of such a type, as occurring in the…
We considered a long-range Ising model under Glauber dynamics and calculated the difference from the mean-field approximation in a finite-size system using perturbation theory. To deal with the BBGKY hierarchy, we assumed that certain types…
We use a Hamiltonian dynamics to discuss the statistical mechanics of long-lasting quasi-stationary states particularly relevant for long-range interacting systems. Despite the presence of an anomalous single-particle velocity distribution,…
In this work, we have employed Monte Carlo calculations to study the Ising model on a 2D additive small-world network with long-range interactions depending on the geometric distance between interacting sites. The network is initially…
Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry…
We extend a recent argument by Ding and Zhuang from nearest-neighbor to long-range interactions and prove the phase transition in a class of ferromagnetic random field Ising models. Our proof combines a generalization of Fr\"ohlich-Spencer…
There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…
A relation between O(n) lattice spin models and Ising models defined on the same lattice was recently put forward [L. Casetti, C. Nardini, and R. Nerattini, Phys. Rev. Lett. 106, 057208 (2011)]. Such a relation, inspired by an energy…