Condensation of vortices and disorder parameter in 3d Heisenberg model

The 3d Heisenberg model is studied from a dual point of view. It is shown that the disordered phase corresponds to condensation of vortices in the vacuum, and the critical indices are computed from the corresponding disorder parameter.Comment: LATTICE98(spin

Confinement and monopole condensation: some properties of the disorder parameter

We demonstrate that the disorder parameter $$ to detect dual superconductivity in the confining phase of QCD is the v.e.v. of a magnetically charged, Dirac like, gauge invariant operator $\mu$. We also show that the abelian projection on the lattice is determined up to terms O(a^2) (a = lattice spacing).Comment: Lattice2001(confinement) proceeding

Theory of color confinement: state of the art

The existing evidence for dual superconductivity as mechanism of color confinement is reviewed. We also discuss what is known on the dual excitations, which produce confinement by condensation, and what are the open problem

Magnetic charge superselection in the deconfined phase of Yang-Mills theory

The vacuum expectation value of an operator carrying magnetic charge is studied numerically for temperatures above the deconfinement temperature in SU(2) and SU(3) gauge theory. By analyzing its finite size behaviour, this is found to be exactly zero in the thermodynamical limit for any T > T_c whenever the magnetic charge of the operator is different from zero. These results show that magnetic charge is superselected in the hot phase of quenched QCD.Comment: 4 pages, 6 figures, revtex

A dual view of the 3d Heisenberg model and the abelian projection

The Heisenberg model in 3d is studied from a dual point of view. It is shown that it can have vortex configurations, carrying a conserved charge(U(1) symmetry). Vortices condens in the disordered phase. A disorder parameter \leftangle\mu\rightangle is defined dual to the magnetization \leftangle\vec n\rightangle, which signals condensation of vortices, i.e. spontaneous breaking of the dual U(1) symmetry. This study sheds light on the procedure known as abelian projection in non abelian gauge theories.Comment: LateX, 15 pages, 3 figure

The abelian projection revisited

Abelian projection is reanalysed in the frame of the SU(N) Higgs model. The extension to QCD is discussed. It is shown that dual superconductivity of the vacuum is an intrinsic property independent of the choice of the abelian projection.Comment: 3 pages, 1 figure, Lattice2003(topology

Chiral transition and deconfinement in N_f = 2 QCD

The transition is studied by means of a disorder parameter detecting condensation of magnetic monopoles in the vacuum. The deconfining transition is found to coincide with the chiral transition and the susceptibility \rho, related to the disorder parameter, is consistent with a first order phase transition.Comment: 3 pages, 2 figures. Poster presented at Lattice2004(topology), Fermilab, June 21-26, 200

Dual Superconductivity and Chiral Symmetry in Full QCD

A disorder parameter detecting dual superconductivity of the vacuum is measured across the chiral phase transition in full QCD with two flavours of dynamical staggered fermions. The observed behaviour is similar to the quenched case.Comment: Lattice2001(confinement) proceedings, 3 pages, 2 eps figure

Gauge-invariant quark-antiquark nonlocal condensates in lattice QCD

We study, by numerical simulations on a lattice, the behaviour of the gauge-invariant quark-antiquark nonlocal condensates in the QCD vacuum with dynamical fermions. A determination is also done in the quenched approximation and the results are compared with the full-QCD case. The fermionic correlation length is extracted and compared with the analogous gluonic quantity.Comment: 14 pages, LaTeX file, + 6 PS figure

A test of first order scaling in Nf=2 QCD

We complete our analysis of Nf=2 QCD based on the lattice staggered fermion formulation. Using a series of Monte Carlo simulations at fixed (amq*Ls^yh) one is able to test the universality class with given critical exponent yh. This strategy has been used to test the O(4) universality class and it has been presented at the previous Lattice conferences. No agreement was found with simulations in the mass range amq=[0.01335,0.15] using lattices with Ls=16 up to 32 and Lt=4. With the same strategy, we now investigate the possibility of a first order transition using a new set of Monte Carlo data corresponding to yh=3 in the same mass and volume range as the one used for O(4). A substantial agreement is observed both in the specific heat scaling and in the scaling of the chiral condensate, while the chiral susceptibilities still presents visible deviation from scaling in the mass range explored.Comment: 5 pages, 6 figures, Presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German