Related papers: Notes on the Statistical Mechanics of Systems with…
We study correlations in fermionic lattice systems with long-range interactions in thermal equilibrium. We prove a bound on the correlation decay between anti-commuting operators and generalize a long-range Lieb-Robinson type bound. Our…
Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…
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…
A field-theoretical description of the behavior of a disordered Ising system with long-range interaction is presented. The description is performed in the two-loop approximation in three dimensions using the Pade-Borel resummation…
We study non-equilibrium properties of a chain of $N$ oscillators with both long-ranged harmonic interactions and long-range conservative noise that exchange momenta of particle pairs. We derive exact expressions for the (deterministic)…
The relaxation to equilibrium of lattice systems with long-range interactions is investigated. The timescales involved depend polynomially on the system size, potentially leading to diverging equilibration times. A kinetic equation for…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Gravitational and electrostatic interactions are fundamental examples of systems with long-range interactions. Equilibrium properties of simple models with long-range interactions are well understood and exhibit exotic behaviors : negative…
The critical behaviour of the one-dimensional q-state Potts model with long-range interactions decaying with distance r as $r^{-(1+\sigma)}$ has been studied in the wide range of parameters $0 < \sigma \le 1$ and $\frac{1}{16} \le q \le…
We obtain exact analytical results for lattices of maps with couplings that decay with distance as $r^{-\alpha}$. We analyze the effect of the coupling range on the system dynamics through the Lyapunov spectrum. For lattices whose elements…
We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian Mean Field model as a case study. We show that an abundance of regular trajectories, associated with invariant tori of the single-particle…
Systems of identical particles possessing non-local interactions are capable of exhibiting extra-classical properties beyond the characteristic quantum length scales. This letter derives the dynamics of such systems in the non-relativistic…
We analyse the statistical physics of a two dimensional lattice based gas with long range interactions. The particles interact in a way analogous to Queens on a chess board. The long range nature of the interaction gives the mathematics of…
Long-ranged, or power-law, behavior of correlation functions in both space and time is discussed for classical systems and for quantum systems at finite temperature, and is compared with the corresponding behavior in quantum systems at zero…
We investigate the ground-state properties of the XXZ model with $1/r^{\alpha}$ interactions, describing spins interacting with long-range (LR) transverse (XX) ferromagnetic interactions and longitudinal (Z) antiferromagnetic interactions,…
We study the dynamics of density fluctuations in purely diffusive systems away from equilibrium. Under some conditions the static density correlation function becomes long-ranged. We then analyze this behavior in the framework of…
The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a…
We consider quantum many-body dynamics under quantum measurements, where the measurement-induced phase transitions (MIPs) occur when changing the frequency of the measurement. In this work, we consider the robustness of the MIP for…
We describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system…
The introduction of decaying long-range (LR) interactions $1/r^{d+\sigma}$ has drawn persistent interest in understanding how system properties evolve with $\sigma$. The Sak's criterion and the extended Mermin-Wagner theorem have gained…