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Register a new userFour-point interfacial correlation functions in two dimensions. Exact results from field theory and numerical simulations
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We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip and found to be in excellent agreement with high-precision Monte Carlo simulations.
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We consider near-critical two-dimensional statistical systems at phase coexistence on the half plane with boundary conditions leading to the formation of a droplet separating coexisting phases. General low-energy properties of two-dimensional field theories are used in order to find exact analytic results for one- and two-point correlation functions of both the energy density and order parameter fields. The subleading finite-size corrections are also computed and interpreted within an exact probabilistic picture in which interfacial fluctuations are characterized by the probability density of a Brownian excursion. The analytical results are compared against high-precision Monte Carlo simulations we performed for the specific case of the Ising model. The numerical results are found to be in good agreement with the analytic results in absence of adjustable parameters. The explicit analysis of the closed-form expression for order parameter correlations reveals the long-ranged character of interfacial correlations and their confinement within the interfacial region. The analysis of correlations is then carried out in momentum space through the notion of interface structure factor, which we extend to the case of systems bounded by a flat wall. The presence of the wall and its associated entropic repulsion leads to a specific term in the interface structure factor which we identify.
We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation of the order parameter field. Finite-size corrections and mixed correlations involving the stress tensor trace are also discussed. As an explicit illustration of the technique, we provide a closed-form expression for a three-point correlation function and illustrate the explicit form of the long-ranged interfacial fluctuations as well as their confinement within the interfacial region.
Two-loop Feynman integrals of the massive $phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric functions. A number of interesting and useful relations is given for these integrals as well as for several special mathematical functions and constants.
Critical two-point correlation functions in the continuous and lattice phi^4 models with scalar order parameter phi are considered. We show by different non-perturbative methods that the critical correlation functions <phi^n(0) phi^m(x)> are proportional to <phi(0) phi(x)> at |x| --> infinity for any positive odd integers n and m. We investigate how our results and some other results for well-defined models can be related to the conformal field theory (CFT), considered by Rychkov and Tan, and reveal some problems here. We find this CFT to be rather formal, as it is based on an ill-defined model. Moreover, we find it very unlikely that the used there equation of motion really holds from the point of view of statistical physics.
We show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench), can be described by means of quantum field theory. In the case when the corresponding theory is conformal, we study the evolution of the entanglement entropy for different bi-partitions of the line. We also consider the behavior of one- and two-point correlation functions. All our findings may be explained in terms of a picture, that we believe to be valid more generally, whereby quasiparticles emitted from the joining point at the initial time propagate semiclassically through the system.
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