ﻻ يوجد ملخص باللغة العربية
We consider the weakly coupled $phi^4 $ theory on $mathbb Z^4 $, in a weak magnetic field $h$, and at the chemical potential $ u_c $ for which the theory is critical if $h=0$. We prove that, as $hto 0$, the magnetization of the model behaves as $(hlog h^{-1})^{frac 13} $, and so exhibits a logarithmic correction to mean field scaling behavior. This result is well known to physicists, but had never been proven rigorously. Our proof uses the classic construction of the critical theory by Gawedzki and Kupiainen, and a cluster expansion with large blocks.
We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging transfer
We define a finite size renormalization scheme for $phi^4$ theory which in the thermodynamic limit reduces to the standard scheme used in the broken phase. We use it to re-investigate the question of triviality for the four dimensional infinite bare
The 1-arm exponent $rho$ for the ferromagnetic Ising model on $mathbb{Z}^d$ is the critical exponent that describes how fast the critical 1-spin expectation at the center of the ball of radius $r$ surrounded by plus spins decays in powers of $r$. Sup
Four generalizations of the Phase Integral Approximation (PIA) to sets of N ordinary differential equations of the Schroedinger type: u_j(x) + Sum{k = 1 to N} R_{jk}(x) u_k(x) = 0, j = 1 to N, are described. The recurrence relations for higher order
We consider the $n$-component $|varphi|^4$ lattice spin model ($n ge 1$) and the weakly self-avoiding walk ($n=0$) on $mathbb{Z}^d$, in dimensions $d=1,2,3$. We study long-range models based on the fractional Laplacian, with spin-spin interactions or