We apply the Dynamical Mean Field (DMFT) approximation to the real, scalar ϕ 4 quantum field theory. By comparing to lattice Monte Carlo calculations, perturbation theory and standard mean field theory, we test the quality of the approximation in two, three, four and five dimensions. The quantities considered in these tests are the critical coupling for the transition to the ordered phase and the associated critical exponents ν and β. We also map out the phase diagram in the most relevant case of four dimensions. In two and three dimensions, DMFT incorrectly predicts a first order phase transition for all bare quartic couplings, which is problematic, because the second order nature of the phase transition of lattice ϕ 4 -theory is crucial for taking the continuum limit. Nevertheless, by extrapolating the behavior away from the phase transition, one can obtain critical couplings and critical exponents. They differ from those of mean field theory and are much closer to the correct values. In four dimensions the transition is second order for small quartic couplings and turns weakly first order as the coupling increases beyond a tricritical value. In dimensions five and higher, DMFT gives qualitatively correct results, predicts reasonable values for the critical exponents and considerably more accurate critical couplings than standard mean field theory. The approximation works best for small values of the quartic coupling. We investigate the change from first to second order transition in the local limit of DMFT which is computationally much cheaper. We also discuss technical issues related to the convergence of the non-linear self-consistency equation solver and the solution of the effective single-site model using Fourier-space Monte Carlo updates in the presence of a ϕ 4 -interaction.arXiv:1305.7136v2 [hep-lat]

We report on recent progress of the implementation of the similarity renormalization group (SRG) for three-body interactions in a one-dimensional, bosonic model system using the plane wave basis. We discuss our implementation of the flow equations and show results that confirm that results in the three-body sector remain unchanged by the transformation of the Hamiltonian. We also show how the SRG transformation decouples low-from high-momentum nodes in the three-body sector and therefore simplifies the numerical calculation of observables.Let us denote with H s the transformed (and initially unknown) Hamiltonian where s denotes the so-called flow arXiv:1107.3064v1 [nucl-th]

Abstract:We investigate the phase diagram of the compact U(1) lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. However, since the monopoles do not influence the long-distance properties of the Coulomb phase, the physics is smooth across the singularity in the monopole density. The topological action offers an algorithmic advantage for the computation of the free energy.

Using Monte Carlo simulations and extended mean field theory calculations we show that the 3-dimensional Z 3 spin model with complex external fields has nonmonotonic spatial correlators in some regions of its parameter space. This model serves as a proxy for heavy-dense QCD in (3 + 1) dimensions. Non-monotonic spatial correlators are intrinsically related to a complex mass spectrum and a liquid-like (or crystalline) behavior. A liquid phase could have implications for heavy-ion experiments, where it could leave detectable signals in the spatial correlations of baryons.

Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We remark, as has been noted before, that the discussion of vacuum stability is completely modified in the presence of a ϕ 6 term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass M h ¼ 125 GeV. By taking a ϕ 6 interaction in the Higgs potential as a proxy for a UV completion of the standard model, the transition becomes stronger and turns first order if the scale of new physics, i.e., the mass of the lightest mediator particle, is around 1.5 TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.