Related papers: Universality under conditions of self-tuning
Finite-size scaling above the upper critical dimension is a long-standing puzzle in the field of Statistical Physics. Even for pure systems various scaling theories have been suggested, partially corroborated by numerical simulations. In…
The universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality, is…
Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we use the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete dynamical…
The quantum phase transition of the one-dimensional long-range transverse-field Ising model is explored by combining the quantum Monte Carlo method and stochastic parameter optimization, specifically achieved by tuning correlation ratios so…
We study the critical behavior of the $d=3$ Ising model with bond randomness through extensive Monte Carlo simulations and finite-size scaling techniques. Our results indicate that the critical behavior of the random-bond model is governed…
Quantum phase transitions are usually classified into discrete universality classes that typically only depend on symmetries and spatial dimensionalities. In this Letter, we demonstrate an opportunity to continuously vary the critical…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
Homogeneous nucleation of a new phase near an Ising-like critical point of another phase transition is studied. A scaling analysis shows that the free energy barrier to nucleation contains a singular term with the same scaling as the order…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
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 use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes…
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…
Energy eigenvalues and order parameters are calculated by exact diagonalization for the transverse Ising model on square lattices of up to 6x6 sites. Finite-size scaling is used to estimate the critical parameters of the model, confirming…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard…
We demonstrate, by means of a convolutional neural network, that the features learned in the two-dimensional Ising model are sufficiently universal to predict the structure of symmetry-breaking phase transitions in considered systems…
By solving the Schr\"odinger equation one obtains the whole energy spectrum, both the bound and the continuum states. If the Hamiltonian depends on a set of parameters, these could be tuned to a transition from bound to continuum states.…
In the finite-size scaling analysis of Monte Carlo data, instead of computing the observables at fixed Hamiltonian parameters, one may choose to keep a renormalization-group invariant quantity, also called phenomenological coupling, fixed…
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…