arXiv subjects
Publications and source records attributed to V. K. Mitrjushkin.
In quenched lattice QCD with standard Wilson fermions the quark propagator is computed very close to the chiral limit in the zero-temperature case. Starting from our experience with lattice QED we employ a modified statistical method in order to estimate reliably hadron masses.
By comparison of the quenched and full formulations of compact QED with Wilson fermions we single out the effects of dynamical fermions on the `chiral transition line' within the confinement phase. It is shown that this line cannot correspond to the chiral limit of the theory for all values of the gauge coupling. This seems to imply the existence of tri-critical points in this theory, the phase structure of which has a close similarity to QCD at finite temperature.
We investigate the propagators of 4D SU(2) gauge theory in Landau gauge by Monte Carlo simulations. To be able to compare with perturbative calculations we use large $β$ values. There the breaking of the Z(2) symmetry causes large effects for all four lattice directions and doing the analysis in the appropriate state gets important. We find that the gluon propagator in the weak-coupling limit is strongly affected by zero-momentum modes.
We study the heavy charge potential in the Coulomb phase of pure gauge compact U(1) theory on the lattice. We calculate the static potential $V_W(T,{\vec R})$ from Wilson loops on a $16^3 \times 32$ lattice and compare with the predictions of lattice perturbation theory. We investigate finite size effects and, in particular, the importance of non-Coulomb contributions to the potential. We also comment on the existence of a maximal coupling in the Coulomb phase of pure gauge U(1) theory.
We compare the approach to the chiral transition line $~κ_c(\bt)~$ in quenched and full compact lattice QED with Wilson fermions within the confinement phase, especially in the pseudoscalar sector of the theory. We show that in the strong coupling limit ($β=0$) the quenched theory is a good approximation to the full one, in contrast to the case of $β=0.8$. At the larger $β$-value the transition in the full theory is inconsistent with the zero--mass limit of the pseudoscalar particle, thus prohibiting the definition of a chiral limit.
The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non--abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed.
The chiral limit $~κ\simeq κ_c(β)~$ in lattice gauge theories with Wilson fermions and problems related to near--to--zero ('exceptional') eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $~\mpr_π~$ for the calculation of the pseudoscalar mass $~m_π~$ is proposed which does not suffer from 'divergent' contributions at $κ\simeq κ_c(β)$. We conclude that the main contribution to the pion mass comes from larger modes, and 'exceptional' eigenvalues play {\it no} physical role. The behaviour of the subtracted chiral condensate $~\langle \psb ψ\rangle_{subt}~$ near $~κ_c(β)~$ is determined. We observe a comparatively large value of $~\langle \psb ψ\rangle_{subt} \cdot Z_P^{-1}~$, which could be interpreted as a possible effect of the quenched approximation.
It is shown that the zero--momentum modes can strongly affect the values of the masses, for example the magnetic screening mass $m_m$, calculated from gauge--dependent correlators with zero momentum.
We compare different conjugate gradient -- like matrix inversion methods (CG, BiCGstab1 and BiCGstab2) employing for this purpose the compact lattice quantum electrodynamics (QED) with Wilson fermions. The main goals of this investigation are the CPU time efficiency of the methods as well as the influence of machine precision on the reliability of (physical) results especially close to the 'critical' line $~κ_c(\bt)$.
We investigate a model of a U(1)-Higgs theory on the lattice with compact gauge fields but completely suppressed (elementary) monopoles. We study the model at two values of the quartic Higgs self-coupling, a strong coupling, $λ= 3.0$, and a weak coupling, $λ=0.01$. We map out the phase diagrams and find that the monopole suppression eliminated the confined phase of the standard lattice model at strong gauge coupling. We perform a detailed analysis of the static potential and study the mass spectrum in the Coulomb and Higgs phases for three values of the gauge coupling. We also probe the existence of a scalar bosonium to the extent that our data allow and conclude that further investigations are required in the Coulomb phase.
The phase diagram for the compact lattice QED with Wilson fermions is shown. We discuss different methods for the calculation of the 'pion' mass $m_π$ near the chiral transition point $κ_c(β)$.
We study the phase structure and the chiral limit of $4d$ compact lattice QED with Wilson fermions (both dynamical and quenched). We use the standard Wilson gauge action and also a modified one suppressing lattice artifacts. Different techniques and observables to locate the chiral limit are discussed.
Different formulations of the $4d$ compact lattice QED with staggered fermions (standard Wilson and modified by suppression of lattice artifacts) are investigated by Monte Carlo simulations within the quenched approximation. We show that after suppressing lattice artifacts the system undergoes a phase transition from the Coulomb phase into a presumably weakly chirally broken phase only at (unphysical) negative $β$--values.
We study the phase structure and chiral limit of $4d$ compact lattice QED with Wilson fermions (both dynamical and quenched). We use the standard Wilson action (WA) and also the modified action (MA) with some lattice artifacts suppressed. We show that lattice artifacts influence the distributions of eigenvalues $~λ_i~$ of the fermionic matrix especially for small values of $~λ_i~$. Our main conclusion is that the chiral limit of compact QED can be efficiently located using different techniques. Sorry, figures are not included and can be sent by ordinary mail or Fax.
We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the $2d$ Ising model and in finite temperature $SU(2)$ gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for $SU(2)$ a Debye screening mass $~μ_D/T\approx4~$, independent of the volume. Sorry, figures are not included and can be sent by ordinary mail.
Photon correlators in $~U(1)~$ pure gauge theory for different lattice actions are considered under the Lorentz gauge condition. They are shown to depend strongly on the gauge fixing ambiguity and on the corresponding existence of Dirac sheets. For the Coulomb phase a gauge fixing algorithm is proposed which avoids Dirac sheets and allows to find the global extremum of the non-local gauge condition. Sorry, figures are not included and can be sent by ordinary mail.
We study properties of the compact $~4D~$ $U(1)$ lattice gauge theory with monopoles {\it removed}. Employing Monte Carlo simulations we calculate correlators of scalar, vector and tensor operators at zero and nonzero momenta $~\vec{p}~$. We confirm that the theory without monopoles has no phase transition, at least, in the interval $~0 < β\leq 2~$. There the photon becomes massless and fits the lattice free field theory dispersion relation very well. The energies of the $~0^{++}~$, $~1^{+-}~$ and $~2^{++}~$ states show a rather weak dependence on the coupling in the interval of $~β~$ investigated, and their ratios are practically constant. We show also a further modification of the theory suppressing the negative plaquettes to improve drastically the overlap with the lowest states (at least, for $~J=1$).