Related papers: Finite-size scaling in systems with long-range int…
The establishment of the Wilson-Fisher fixed point (WFP) for $O(n)$ spin models in $d=4-\epsilon$ dimensions stands as a cornerstone of the renormalization group (RG) theory for critical phenomena. However, when long-range (LR)…
Infinite-range interactions are known to facilitate the production of highly entangled states with applications in quantum information and metrology. However, many experimental systems have interactions that decay with distance, and the…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^{\alpha}$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact…
The critical behavior of the chiral quark-meson model is studied within the Functional Renormalization Group (FRG). We derive the flow equation for the scale dependent thermodynamic potential at finite temperature and density in the…
Pinning models are built from discrete renewal sequences by rewarding (or penalizing) the trajectories according to their number of renewal epochs up to time $N$, and $N$ is then sent to infinity. They are statistical mechanics models to…
The search for the QCD critical end point (CEP) is a major objective of contemporary heavy-ion physics, motivating the study of fluctuation observables that are sensitive to critical dynamics. In particular, baryon-number fluctuations…
To study the kinetics of phase separation in active matter systems, we consider models that impose a Vicsek-type self-propulsion rule on otherwise passive particles interacting via the Lennard-Jones potential. Two types of kinetics are of…
The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general…
Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting…
Scaling, hyperscaling and finite-size scaling were long considered problematic in theories of critical phenomena in high dimensions. The scaling relations themselves form a model-independent structure that any model-specific theory must…
The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order…
We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from…
We investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction, $J_{ij} = |\vec{r}_i -\vec{r}_j|^{-(d+\sigma)}$, where…
In this work we consider the 1-component real scalar $\phi^4$ theory in 4 space-time dimensions on the lattice and investigate the finite size scaling of thermodynamic quantities to study whether the thermodynamic limit is attained. The…
We compare the critical behavior of the short-range Ising spin glass with a spin glass with long-range interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the long-range model for which…
The slowly evolving gauge coupling of gauge-fermion systems near the conformal window makes numerical investigations of these models challenging. We consider finite size scaling and show that this often used technique leads to inconsistent…
We study the scaling properties of Higgs-Yukawa models. Using the technique of Finite-Size Scaling, we are able to derive scaling functions that describe the observables of the model in the vicinity of a Gaussian fixed point. A feasibility…
We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by…
Systems with an O(n) symmetrical Hamiltonian are considered in a $d$-dimensional slab geometry of macroscopic lateral extension and finite thickness $L$ that undergo a continuous bulk phase transition in the limit $L\to\infty$. The…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…