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Correlation functions in the O(n) models below the critical temperature are considered. Based on Monte Carlo (MC) data, we confirm the fact stated earlier by Engels and Vogt, that the transverse two-plane correlation function of the O(4) model for lattice sizes about L=120 and small external fields h is very well described by a Gaussian approximation. However, we show that fits of not lower quality are provided by certain non-Gaussian approximation. We have also tested larger lattice sizes, up to L=512. The Fourier-transformed transverse and longitudinal two-point correlation functions have Goldstone mode singularities in the thermodynamic limit at k --> 0 and h=+0, i.e., G_perp(k) = a k^{-lambda_perp} and G_parallel(k) = b k^{-lambda_parallel}, respectively. Here a and b are the amplitudes, k is the magnitude of the wave vector. The exponents lambda_perp, lambda_parallel and the ratio b M^2/a^2, where M is the spontaneous magnetization, are universal according to the GFD (grouping of Feynman diagrams) approach. Here we find that the universality follows also from the standard (Gaussian) theory, yielding b M^2/a^2 = (n-1)/16. Our MC estimates of this ratio are 0.06 +/- 0.01 for n=2, 0.17 +/- 0.01 for n=4 and 0.498 +/- 0.010 for n=10. According to these and our earlier MC results, the asymptotic behavior and Goldstone mode singularities are not exactly described by the standard theory. This is expected from the GFD theory. We have found appropriate analytic approximations for G_perp(k) and G_parallel(k), well fitting the simulation data for small k. We have used them to test the Patashinski--Pokrovski relation and have found that it holds approximately.
Monte Carlo (MC) analysis of the Goldstone mode singularities for the transverse and the longitudinal correlation functions, behaving as G_{perp}(k) simeq ak^{-lambda_{perp}} and G_{parallel}(k) simeq bk^{-lambda_{parallel}} in the ordered phase at k
Power-law singularities and critical exponents in n-vector models are considered from different theoretical points of view. It includes a theoretical approach called the GFD (grouping of Feynman diagrams) theory, as well as the perturbative renormali
We review some recent results concerning the quantitative analysis of the universality classes of two-dimensional statistical models near their critical point. We also discuss the exact calculation of the two--point correlation functions of disorder
Exact results on particle-densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair-annihilation whe
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear