Related papers: Lattice Computation of the Effective Potential in …
We present a critical reappraisal of the available results on the broken phase of $\lambda(\Phi^4)_4$ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous…
The strong evidence for the `triviality' of (lambda Phi^4)_4 theory is not incompatible with spontaneous symmetry breaking. Indeed, for a `trivial' theory the effective potential should be given exactly by the classical potential plus the…
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 generally accepted ``triviality'' of $\lambda\Phi^4$ theories does not forbid Spontaneous Symmetry Breaking but implies a trivially free shifted field which becomes effectively governed by a quadratic hamiltonian. As a consequence, one…
There are two physically different interpretations of ``triviality'' in $(\lambda\Phi^4)_4$ theories. The conventional description predicts a second-order phase transition and that the Higgs mass $m_h$ must vanish in the continuum limit if…
We present a detailed discussion of Spontaneous Symmetry Breaking (SSB) in $(\lambda\Phi^4)_4$. In the usual approach, inspired by perturbation theory, one predicts a second-order phase transition, the Higgs mass $m_h$, related to the value…
We obtain effective potential of $O(N)$-symmetric $\phi^4$ theory for large $N$ starting with a finite lattice system and taking the thermodynamic limit with great care. In the thermodynamic limit, it is globally real-valued and convex in…
The `triviality' of $\Phi^4_4$ has been traditionally interpreted within perturbation theory where the prediction for the Higgs boson mass depends on the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially assumes that…
The `triviality' of $\Phi^4_4$ has been traditionally interpreted within perturbation theory where the prediction for the Higgs boson mass depends on the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially assumes that…
We investigate the possibility of using the 4 dimensional $O(4)$ symmetric $\phi^4$ model as an effective theory for the sigma-pion system. We carry out lattice Monte Carlo simulations to establish the triviality bound in the case of…
The 1-loop effective potential in a scalar theory with quartic interaction on the space $M^{4} \times T^{n}$ for $n=2$ is calculated and is shown to be unbounded from below. This is an indication of a possible instability of the vacuum of…
Recent lattice data for the effective potential of lambda Phi^4 theory fits the massless one-loop formula with amazing precision. Any corrections are at least 100 times smaller than is reasonable, perturbatively. This is strong evidence for…
Recent lattice simulations of $(\lambda \Phi^4)_4$ theories in the broken phase show that : a) the shifted field propagator is well reproduced by the simple 2-parameter form ${{Z_{\rm prop}}\over{p^2 + M^2_h}}$ at finite momenta but…
Branchina et al and Consoli have recently shown that the one-loop effective potential (1LEP) of massless lambda-phi**4 theory can be renormalized in two distinct ways. One of these is the conventional renormalization of Coleman and…
Using lattice simulations of a one-component $(\lambda \Phi^4)_4$ theory, we have measured the energy spectrum $\omega({\mathbf{k}})$ in the broken phase at various lattice sizes. Our data show that the energy-gap $\omega(0)$ is {\it not}…
We study the $O(4)$-symmetric $ \Phi^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $\lambda$. A high precision Monte Carlo simulation is performed by…
We calculate the explicit expression of the effective potential in a $\lambda\phi^4$ theory at finite temperature in a static universe for arbitrary spacetime dimensions (2\leq D < 5). To study the combined effects of the temperature and…
We argue that massless (lambda Phi^4)_4 is "trivial" without being entirely trivial. It has a non-trivial effective potential which leads to spontaneous symmetry breaking, but the particle excitations above the broken vacuum are…
We study the $2$-component $\phi^4$ model on the simple cubic lattice in the presence of a cubic, or equivalently, a $\mathbb{D}_4$ invariant perturbation. To this end, we perform Monte Carlo simulations in conjunction with a finite size…
An alternative model to the trivial $\phi^4$-theory of the standard model of weak interactions is suggested, which embodies the Higgs-mechanism, but is free of the conceptual problems of standard $\phi ^4$-theory. We propose a N-component,…