Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userTriviality of $phi^4_4$ in the broken phase revisited
119
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 coupling (Ising) limit. The relevant observables all rely on two-point functions and are very suitable for a precise estimation with the worm algorithm. This contribution updates an earlier publication by analysing a much larger dataset.
rate research
Read More
We study the standard one-component $varphi^4$-theory in four dimensions. A renormalized coupling is defined in a finite size renormalization scheme which becomes the standard scheme of the broken phase for large volumes. Numerical simulations are reported using the worm algorithm in the limit of infinite bare coupling. The cutoff dependence of the renormalized coupling closely follows the perturbative Callan Symanzik equation and the triviality scenario is hence further supported.
Quantum electrodynamics is considered to be a trivial theory. This is based on a number of evidences, both numerical and analytical. One of the strong indications for triviality of QED is the existence of the Landau pole for the running coupling. We show that by treating QED as the leading order approximation of an effective field theory and including the next-to-leading order corrections, the Landau pole is removed. Therefore, we conclude that the conjecture, that for reasons of self-consistency, QED needs to be trivial is a mere artefact of the leading order approximation to the corresponding effective field theory.
We compute numerically the effective potential for the $(lambda Phi^4)_4$ theory on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. Two different methods for obtaining the effective potential were used as a control on the results. We compare our numerical results with three theoretical descriptions. Our lattice data are in quite good agreement with the ``Triviality and Spontaneous Symmetry Breaking picture.
Worm methods to simulate the Ising model in the Aizenman random current representation including a low noise estimator for the connected four point function are extended to allow for antiperiodic boundary conditions. In this setup several finite size renormalization schemes are formulated and studied with regard to the triviality of phi^4 theory in four dimensions. With antiperiodicity eliminating the zero momentum Fourier mode a closer agreement with perturbation theory is found compared to the periodic torus.
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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
