Related papers: The lambda Phi^4 Miracle: lattice data and the zer…
We consider $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hat{\lambda}$ the (negative) critical bare mass $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ where the…
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…
The standard lattice perturbation theory leads to the asymptotic series because of the incorrect interchange of the summation and integration. However, changing the initial approximation of the perturbation theory, one can generate the…
We present a self--consistent solution of the finite temperature gap--equation for $\lambda \Phi^4$ theory beyond the Hartree-Fock approximation using a composite operator effective action. We find that in a spontaneously broken theory not…
We investigate the non-perturbative features of $\phi^4_2$ theory in two dimensions, using Monte Carlo lattice methods. In particular we determine the ratio $f_0 \equiv g/\mu^2$, where g is the unrenormalised coupling, in the infinite…
In theories with spontaneous symmetry breaking, the conventional effective potential possesses a defective loop expansion. For such theories, the exact effective potential $V(\phi_c,T)$ is real and convex, but its perturbative series is…
Using a new scaling limit as well as a new cut-off procedure, we show that $\phi^4$ theory on noncommutative ${\bf R}^4$ can be obtained from the corresponding theory on fuzzy ${\bf S}^2 \times {\bf S}^2$. The star-product on this…
The two loop effective potential of massless $\lambda\phi^4$ theory was presented in several regularization and renormalization prescriptions and the dynamical symmetry breaking solution was obtained in strong coupling situation in several…
The functional formulation and one-loop effective action for scalar self-interacting theory non-linearly coupled with some power of the curvature are studied. After the explicit one-loop renormalization at weak curvature, we investigated…
Precision tests of QCD perturbation theory are not readily available from experimental data. The main reasons are systematic uncertainties due to the confinement of quarks and gluons, as well as kinematical constraints which limit the…
Massless $\phi^{4}$-theory is investigated in zero and four space-time dimensions. Path-integral linearisation of the $\phi ^{4}$-interaction defines an effective theory, which is investigated in a loop-expansion around the mean field. In…
Assuming triviality of the 4-dimensional $\lambda \phi ^4$-theory we compute the effective potential by means of a self consistent Feynman-Bogoliubov method. This potential $U_{eff}^{FB}$ depends on a UV-cutoff, which is fixed by a…
A loop expansion is implemented based on the path integral quantization of the light-cone $\phi^4$ field theory in 1+1 dimensions. The effective potential as a function of the zero-mode field $\omega$ is calculated up to two loop order and…
We present here a new MC study of ISB at finite temperature in a $Z_2\times Z_2$ $\lambda\phi^4$ model in four dimensions. The results of our simulations, even if not conclusive, are favourable to ISB. Detection of the effect required…
We calculate the one-loop effective potential at finite temperature for a system of massless scalar fields with quartic interaction $\lambda\phi^4$ in the framework of the boundary effective theory (BET) formalism. The calculation relies on…
The consistency condition, which guarantees a well organized small-coupling asymptotic expansion for the thermodynamics of massless $\phi^4$-theory, is generalized to any desired order of the perturbative treatment. Based on a strong…
We investigate whether the seven-loop beta function of the $\lambda \phi^4_4$ theory exhibits evidence for an ultraviolet zero. In addition to a direct analysis of the beta function, we calculate and study Pad\'e approximants and discuss…
The tensor renormalization group attracts great attention as a new numerical method that is free of the sign problem. In addition to this striking feature, it also has an attractive aspect as a coarse-graining of space-time; the…
The spontaneous symmetry breaking in noncommutative $\lambda\Phi^4$ theory has been analyzed by using the formalism of the effective action for composite operators in the Hartree-Fock approximation. It turns out that there is no phase…
The L-loop 4-point ladder diagram of massless phi^3 theory is finite when all 4 legs are off-shell and is given in terms of polylogarithms with orders ranging from L to 2L. We obtain the exact solution of the linear Dyson-Schwinger equation…