arXiv subjects
Publications and source records attributed to V. Laliena.
We compute the fixed point action for the Schwinger model through an expansion in the gauge field. The calculation allows a check of the locality of the action. We test its perfection by computing the 1-loop mass gap at finite spatial volume.
We consider some radiative corrections to the lowest order annihilation diagram for the orthopositronium decay rate. The insertion of the renormalized vertex correction in the annihilation graph gives $1.6283 (α/π)^2 Γ_0$. We compute also the contribution of the square of the lowest order annihilation amplitude, which turns out to be $0.1702 (α/π)^2 Γ_0$. Finally, we obtain a term $α^2 \lnαΓ_0$ arising from the correction to the light-light scattering block due to the exchange of one coulombic photon, in agreement with earlier computations.
We report the results of a measurement of susceptibilities in noncompact $QED_4$ in $8^4, 10^4$ and $12^4$ lattices. Due to the potentialities of the $MFA$ approach, we have done simulations in the chiral limit which are therefore free from arbitrary mass extrapolations. Our results in the Coulomb phase show unambiguously that the susceptibility critical exponent $γ=1$ independently of the flavour symmetry group. The critical couplings extracted from these calculations are in perfect agreement with previous determinations based on the fermion effective action and plaquette energy, and outside the predictions of a logarithmically improved scalar mean field theory by eight standard deviations.
We analyse the phase diagram of the lattice gauged Nambu-Jona Lasinio model with the help of a mean field approximation plus numerical simulations. We find a phase transition line in the coupling parameters space separating the chirally broken phase from the symmetric phase, which is in good qualitative agreement with results obtained in the quenched-ladder approximation. The mean field approximation relates the critical exponents along the continuous phase transition line with the mass dependence of the chiral condensate in the Coulomb phase of standard noncompact $QED$. Our numerical results for noncompact $QED$ strongly suggest non mean field exponents along the critical line.
Using very precise measurements of the critical couplings for the chiral transition of non compact $QED_4$ with up to 8 flavours, we analyse the behaviour of the order parameter at the critical point using the equation of state of a logarithmically improved scalar mean field theory, that of the Nambu-Jona Lasinio theory and a pure power law. The first case is definitively excluded by the numerical data. The stability of the fits for the last two cases, as well as the behaviour with the number of flavours of the exponent of the logarithmic violations to the scaling favour clearly a pure power law scaling with non mean field exponents.
Since four-fermion operators in strongly coupled $QED$ are nonperturbatively renormalizable, we analyze here the phase diagram and critical behaviour of the Gauged Nambu-Jona Lasinio model. Our mean field approximation relates the critical exponents along the continuous phase transition line with the mass dependence of the chiral condensate in the Coulomb phase of standard noncompact $QED$. The numerical results for noncompact $QED$ strongly suggest non mean field exponents along the critical line.
We measure chiral susceptibilities in the Coulomb phase of noncompact QED$_4$ in $8^4, 10^4$ and $12^4$ lattices. The MFA approach allows simulations in the chiral limit which are therefore free from arbitrary mass extrapolations. Using the critical couplings extracted from these calculations, we study the critical behaviour of the chiral condensate, which we find in disagreement with the predictions of logarithmically improved scalar Mean Field theory.
We present a detailed analysis, in the framework of the MFA approach, of the critical behaviour of the lattice Schwinger model with Wilson fermions on lattices up to $24^2$, through the study of the Lee-Yang zeros and the specific heat. We find compelling evidence for a critical line ending at $κ= 0.25$ at large $β$. Finite size scaling analysis on lattices $8^2,12^2,16^2, 20^2$ and $24^2$ indicates a continuous transition. The hyperscaling relation is verified in the explored $β$ region.
The MFA approach for simulations with dynamical fermions in lattice gauge theories allows in principle to explore the parameters space of the theory (e.g. the $β, m$ plane for the study of chiral condensate in QED) without the need of computing the fermionic determinant at each point. We exploit this possibility for extracting both the renormalization group trajectories ("constant physics lines") and the scaling function, and we test it in the Schwinger Model. We discuss the applicability of this method to realistic theories.
The Microcanonical Fermionic Average method has been used so far in the context of lattice models with phase transitions at finite coupling. To test its applicability to Asymptotically Free theories, we have implemented it in QED$_2$, \it i.e.\rm the Schwinger Model. We exploit the possibility, intrinsic to this method, of studying the whole $β, m$ plane at negligible computer cost, to follow constant physics trajectories and measure the $m \to 0$ limit of the chiral condensate. We recover the continuum result within 3 decimal places.
We study the phase diagram of non compact $QED_3$ using the $MFA$ method and present evidence for a continuous phase transition line at small $N_f$. We also analyze the chiral structure of the vacuum by means of the computation of the probability distribution function of the order parameter in the exact chiral limit.
The reasons for the feasibility of the Microcanonical Fermionic Average ($MFA$) approach to lattice gauge theory with dynamical fermions are discussed. We then present a new exact algorithm, which is free from systematic errors and convergent even in the chiral limit.