The 4-D Layer Phase as a Gauge Field Localization: Extensive Study of the 5-D Anisotropic U(1) Gauge Model on the Lattice

We study a 4+1 dimensional pure Abelian Gauge model on the lattice with two anisotropic couplings independent of each other and of the coordinates. A first exploration of the phase diagram using mean field approximation and monte carlo techniques has demonstrated the existence of a new phase, the so called Layer phase, in which the forces in the 4-D subspace are Coulomb-like while in the transverse direction (fifth dimension) the force is confining. This allows the possibility of a gauge field localization scheme. In this work the use of bigger lattice volumes and higher statistics confirms the existence of the Layer phase and furthermore clarifies the issue of the phase transitions' order. We show that the Layer phase is separated from the strongly coupled phase by a weak first order phase transition. Also we provide evidence that the Layer phase is separated by the five-dimensional Coulomb phase with a second order phase transition and we give a first estimation of the critical exponents.Comment: 19 pages, 16 figure

Integrable structures in LGTs near the deconfinement transition

In this contribution we review some recent results about the emergence of 2D integrable systems in 3D Lattice Gauge Theories near the deconfinement transition. We focus on some concrete examples involving the flux tube thickness, the ratio of k-string tensions and Polyakov loops correlators in various models.Comment: 8 pages, Poster contribution to the XXVII International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, Chin

The confining string beyond the free-string approximation in the gauge dual of percolation

We simulate five different systems belonging to the universality class of the gauge dual of three-dimensional random percolation to study the underlying effective string theory at finite temperature. All the data for the finite temperature string tension, when expressed by means of adimensional variables, are nicely described by a unique scaling function. We calculate the first few terms of the string tension up to order $T^6$ and compare to different theoretical predictions. We obtain unambiguous evidence that the coefficients of $T^2$ and $T^4$ terms coincide with those of the Nambu-Goto string, as expected, while the $T^6$ term strongly differs and is characteristic of the universality class of this specific gauge theory.Comment: 13 pages, 3 figure

Critical domain walls in the Ashkin-Teller model

We study the fractal properties of interfaces in the 2d Ashkin-Teller model. The fractal dimension of the symmetric interfaces is calculated along the critical line of the model in the interval between the Ising and the four-states Potts models. Using Schramm's formula for crossing probabilities we show that such interfaces can not be related to the simple SLE$_\kappa$, except for the Ising point. The same calculation on non-symmetric interfaces is performed at the four-states Potts model: the fractal dimension is compatible with the result coming from Schramm's formula, and we expect a simple SLE$_\kappa$ in this case.Comment: Final version published in JSTAT. 13 pages, 5 figures. Substantial changes in the data production, analysis and in the conclusions. Added a section about the crossing probability. Typeset with 'iopart

Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks

Lattice QCD at finite density suffers from a severe sign problem, which has so far prohibited simulations of the cold and dense regime. Here we study the onset of nuclear matter employing a three-dimensional effective theory derived by combined strong coupling and hopping expansions, which is valid for heavy but dynamical quarks and has a mild sign problem only. Its numerical evaluations agree between a standard Metropolis and complex Langevin algorithm, where the latter is free of the sign problem. Our continuum extrapolated data clearly show a first order phase transition building up at $\mu_B \approx m_B$ as the temperature approaches zero. An excellent description of the data is achieved by an analytic solution in the strong coupling limit.Comment: Four pages, three figures; uses REVTeX-4. Version accepted by PRL. Title changed upon request by the Editor

Random percolation as a gauge theory

Three-dimensional bond or site percolation theory on a lattice can be interpreted as a gauge theory in which the Wilson loops are viewed as counters of topological linking with random clusters. Beyond the percolation threshold large Wilson loops decay with an area law and show the universal shape effects due to flux tube quantum fluctuations like in ordinary confining gauge theories. Wilson loop correlators define a non-trivial spectrum of physical states of increasing mass and spin, like the glueballs of ordinary gauge theory. The crumbling of the percolating cluster when the length of one periodic direction decreases below a critical threshold accounts for the finite temperature deconfinement, which belongs to 2-D percolation universality class.Comment: 20 pages, 14 figure

Conformal Curves in Potts Model: Numerical Calculation

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the $q$-state Potts model for integer and non-integer values of $q$ on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that this curves can be described by SLE$_{\kappa}$.Comment: 11 Pages, 4 figure

Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks

Lattice QCD at finite density suffers from a severe sign problem, which has so far prohibited simulations of the cold and dense regime. Here we study the onset of nuclear matter employing a three-dimensional effective theory derived by combined strong coupling and hopping expansions, which is valid for heavy but dynamical quarks and has a mild sign problem only. Its numerical evaluations agree between a standard Metropolis and complex Langevin algorithm, where the latter is free of the sign problem. Our continuum extrapolated data approach a first order phase transition at µB ≈ mB as the temperature approaches zero. An excellent description of the data is achieved by an analytic solution in the strong coupling limit. PACS numbers: 05.70. Fh,11.15Ha,12.38.Gc Keywords: QCD phase diagram, lattice gauge theory, sign problem QCD at zero temperature is expected to exhibit the so-called silver blaze property: when a chemical potential for baryon number µ B is switched on in the grand canonical partition function, initially all observables should be completely independent of µ B . This changes abruptly once the chemical potential exceeds a critical value µ Bc , for which the baryon number jumps from zero to a finite value and a transition to a condensed state of nuclear matter takes place. The reason for this behavior is the mass gap in the fermionic spectrum, where the nucleon mass m B represents the lowest baryonic energy that can be populated once µ B ≈ m B . While this picture is easy to see in terms of energy levels of nucleons in a Hamiltonian language, it is elusive in the fundamental formulation of QCD thermodynamics in terms of a path integral. There, chemical potential enters through the Dirac operators of the quark fields, and hence all Dirac eigenvalues are shifted for any value of µ B . The silver blaze property thus requires some exact cancellations for µ B < m B . An analytic derivation of the silver blaze property from the path integral exists only for the related case of finite isospin chemical potential where Bose-Einstein condensation of pions sets in at µ I = m π /2. A numerical demonstration of the effect by means of lattice QCD has so far been impossible due to the so-called sign problem. For finite baryon chemical potential the action becomes complex, prohibiting its use in a Boltzmann factor for Monte Carlo approaches with importance sampling. Several approximate methods have been devised to circumvent this problem. These are valid in the regime µ < ∼ T , where they give consistent results (for a recent review see In this work we show that cold and dense lattice QCD is accessible within a 3d effective theory of Polyakov loops, which has been derived from the full lattice theory with Wilson fermions by means of strong coupling and hopping parameter expansions The lattice QCD partition function with Wilson gauge action S g [U ] and f = 1, . . . , N f quark flavours with Wilson fermion matrix Q(κ f , µ f ) can be written a