arXiv subjects
Publications and source records attributed to Philippe de Forcrand.
We study the phase diagram of the 4d compact U(1) gauge theory as a function of the number of Euclidean time slices. We use the helicity modulus as order parameter to probe the phase transitions. The order of the transition along the phase boundaries is studied and the possibility of a continuum limit is discussed. We present new, strong evidence that the T=0 bulk phase transition is first-order.
We consider the difficulties of finite density QCD from the canonical formalism. We present results for small baryon numbers, where the sign problem can be controlled, in particular by supplementing the mu=0 sampling with imaginary mu ensembles. We initiate the thermodynamic study of few-nucleon systems, starting with the measurement of the free energy of a few baryons in the confined and deconfined phase. We present a simple model for the phase transition, whose results are in good agreement with the literature, but extend to lower temperatures.
We propose a new algorithm to compute the order-order interface tension in SU(N) lattice gauge theories. The algorithm is trivially generalizable to a variety of models, e.g., spin models. In the case N=3, via the perfect wetting hypothesis, we can estimate the order-disorder interface tension. In the case N=4, we study the ratio of dual k-tensions and find that it satisfies Casimir scaling down to T=1.2 T_c.
We discuss the contribution of OZI-suppressed diagrams to the hyperfine splitting of charmonium in lattice QCD. We study valence quark mass regions from strange to charm quark masses. No contribution of the disconnected diagram is seen in the vector meson channel. In the pseudo-scalar channel and for valence quark masses around the strange quark, the disconnected contribution induces a considerable increase of the meson mass. This contribution quickly decreases as the quark mass increases. For charmonium the effect is very small although a decrease of the pseudoscalar mass induced by the disconnected contribution cannot be ruled out.
We consider the 4d compact U(1) gauge theory with extended action S=-beta sum_P cos theta_P -gamma sum_P cos 2 theta_P We give a full characterization of the phase diagram of this model using the notion of flux. The relation with the usual monopole picture is discussed. In analogy with the XY model we consider the helicity modulus \cite{Jose:1977gm} for this theory, and show that it is an order parameter. Analyzing the finite-size effects of the helicity modulus we conclude that the transition is first-order. The value of this order parameter is related to the renormalized coupling beta_R. We measure beta^c_R at the transition point and give a counterexample to its conjectured universal value \cite{Cardy:jg}.
We consider the 4d compact U(1) theory with Wilson action and characterize its phase diagram using the notion of electromagnetic flux, instead of the more usual magnetic monopole. Taking inspiration from the flux picture, we consider the helicity modulus (h.m.) for this theory, and show that it is an order parameter for the confinement deconfinement phase transition. We extend the definition of the h.m. to an Abelian projected Yang-Mills theory, and discuss its behavior in SU(2).
A missing piece is added to the Svetitsky-Yaffe conjecture. The spin model in the same universality class as the (2+1)d SU(4) theory, the 2d Ashkin-Teller model, has a line of continuously varying critical exponents. The exponents measured in the gauge theory correspond best to the Potts point on the Ashkin-Teller line.
While the grand canonical partition function Z_{GC}(mu) with chemical potential mu explicitly breaks the Z_3 symmetry with the Dirac determinant, the canonical partition function at fixed baryon number Z_C(B) is manifestly Z_3-symmetric. We compare Z_{GC}(mu=0) and Z_C(B=0) formally and by numerical simulations, in particular with respect to properties of the deconfinement transition. Differences between the two ensembles, for physical observables characterising the phase transition, vanish with increasing lattice size. We show numerically that the free energy density is the same for both ensembles in the thermodynamic limit.
The subleading term of the heavy quark potential (the analogue of the Luscher term) is computed in a string model for the case of three quarks. It turns out to be positive in 2+1 dimensions, making the potential non-concave as a function of the scale for fixed geometry. The results are compared to numerical simulations of the lattice gauge theory.
An uncontroversial observation of adjoint string breaking is proposed, while measuring the static potential from Wilson loops only. The overlap of the Wilson loop with the broken-string state is small, but non-vanishing, so that the broken-string groundstate can be seen if the Wilson loop is long enough. We demonstrate this in the context of the (2+1)d SU(2) adjoint static potential, using an improved version of the Luscher-Weisz exponential variance reduction. To complete the picture we perform the more usual multichannel analysis with two basis states, the unbroken-string state and the broken-string state (two so-called gluelumps). As by-products, we obtain the temperature-dependent static potential measured from Polyakov loop correlations, and the fundamental SU(2) static potential with improved accuracy. Comparing the latter with the adjoint potential, we see clear deviations from Casimir scaling.
The Villain form of SO(3) lattice gauge theory is studied and compared to Wilson's SU(2) theory. The topological invariants in SO(3) which correspond to twisted boundary conditions in SU(2) are discussed and lattice observables are introduced for them. An apparent SO(3) phase with negative adjoint Polyakov loop is explained in terms of these observables. The electric twist free energy, an order parameter for the confinement-deconfinement transition, is measured in both theories to calibrate the temperature. The results indicate that lattices with about 700^4 sites or larger will be needed to study the SO(3) confined phase. Alternative actions are discussed and an analytic path connecting SO(3) and SU(2) lattice gauge theory at weak coupling is exhibited. The relevance for confinement of the centre of the gauge group is discussed.
A convincing, uncontroversial observation of string breaking, when the static potential is extracted from Wilson loops only, is still missing. This failure can be understood if the overlap of the Wilson loop with the broken string is exponentially small. In that case, the broken string ground state will only be seen if the Wilson loop is long enough. Our preliminary results show string breaking in the context of the 3d SU(2) adjoint static potential, using the Lüscher-Weisz exponential variance reduction approach. As a by-product, we measure the fundamental SU(2) static potential with improved accuracy and see clear deviations from Casimir scaling.
We consider the 4d compact U(1) gauge theory with fundamental-adjoint action on a hypertorus. We give a full characterization of the phase diagram of this model in terms of topological flux sectors.
Lattice gauge theories with gauge groups SO(3) and SU(2) are compared. The free energy of electric twist, an order parameter for the confinement-deconfinement transition which does not rely on centre-symmetry breaking, is measured in both theories. The results are used to calibrate the scale in SO(3).
Compact U(1) theory in 4 dimensions is used to compare the modified iterative and the Laplacian fixing to lattice Landau gauge in a controlled setting, since in the Coulomb phase the lattice theory must reproduce the perturbative prediction. It turns out that on either side of the phase transition clear differences show up and in the Coulomb phase the ability to remove double Dirac sheets proves vital on a small lattice.
We use 't Hooft loops of maximal size on finite lattices to calculate the free energy in the sectors of SU(2) Yang-Mills theory with fixed electric flux as a function of temperature and (spatial) volume. Our results provide evidence for the mass gap. The confinement of electric fluxes in the low temperature phase and their condensation in the high temperature phase are demonstrated. In a surprisingly large scaling window around criticality, the transition is quantitatively well described by universal exponents and amplitude ratios relating the properties of the two phases.
We study the fate of static fundamental charges in the thermodynamic limit from Monte-Carlo simulations of SU(2) with suitable boundary conditions.
We discuss hybrid Monte Carlo algorithms for odd-flavor lattice QCD simulations. The algorithms include a polynomial approximation which enables us to simulate odd-flavor QCD in the framework of the hybrid Monte Carlo algorithm. In order to make the algorithms exact, the correction factor to the polynomial approximation is also included in an economical, stochastic way. We test the algorithms for $n_f=1$, 1+1 and 2+1 flavors and compare results with other algorithms.