Related papers: Conformal perturbation theory
Critical systems are described by conformal field theories, whose dynamics can be exactly solved in two dimensions. In the presence of a boundary, with the so-called method of images it is possible to study the surface critical behaviour of…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
Quantum many body system in equilibrium can be effectively characterized using the framework of quantum statistical mechanics. However, nonequilibrium behaviour of quantum many body systems remains elusive, out of the range of such a well…
This paper explores the numerical conformal bootstrap in general spacetime dimensions through the lens of a distinct category of analytic functionals, previously employed in two-dimensional studies. We extend the application of these…
High accuracy Monte Carlo simulation results for 1024*1024 Ising system with ferromagnetic impurity bonds are presented. Spin-spin correlation function at a critical point is found to be numerically very close to that of a pure system. This…
Ising spin-glass systems with long-range interactions ($J(r)\sim r^{-\sigma}$) are considered. A numerical study of the critical behaviour is presented in the non-mean-field region together with an analysis of the probability distribution…
In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…
Using previous results from boundary conformal field theory and integrability, a phase diagram is derived for the 2 dimensional Ising model at its bulk tri-critical point as a function of boundary magnetic field and boundary spin-coupling…
Moving beyond simple associations, researchers need tools to quantify how variables influence each other in space and time. Correlation functions provide a mathematical framework for characterizing these essential dependencies, revealing…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D version. To this end, we consider respectively, two and three quartic oscillators as the unperturbed system, and…
We study a continuous quantum phase transition that breaks a $Z_2$ symmetry. We show that the transition is described by a new critical point which does not belong to the Ising universality class, despite the presence of well defined…
The presence of both critical behavior and oscillating patterns in brain dynamics is a very interesting issue. In this paper, we consider a model for a neuron population, where each neuron is modeled by an over-damped rotator. We find that…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for…
In this paper, we applied a deep neural network to study the issue of knowledge transferability between statistical mechanics models. The following computer experiment was conducted. A convolutional neural network was trained to solve the…
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 present a conformal theory for intermittent scalar fields. As an example, we consider the energy flux from large to small scales in the developed turbulent flow. The conformal correlation functions are found in the inertial range of…
Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the…