Critical behavior of 3D Z(N) lattice gauge theories at zero temperature

Three-dimensional $Z(N)$ lattice gauge theories at zero temperature are studied for various values of $N$. Using a modified phenomenological renormalization group, we explore the critical behavior of the generalized $Z(N)$ model for $N=2,3,4,5,6,8$. Numerical computations are used to simulate vector models for $N=2,3,4,5,6,8,13,20$ for lattices with linear extension up to $L=96$. We locate the critical points of phase transitions and establish their scaling with $N$. The values of the critical indices indicate that the models with $N>4$ belong to the universality class of the three-dimensional $XY$ model. However, the exponent $\alpha$ derived from the heat capacity is consistent with the Ising universality class. We discuss a possible resolution of this puzzle. We also demonstrate the existence of a rotationally symmetric region within the ordered phase for all $N\geq 5$ at least in the finite volume.Comment: 25 pages, 4 figures, 8 table

The phase transitions in 2D Z(N) vector models for N>4

We investigate both analytically and numerically the renormalization group equations in 2D Z(N) vector models. The position of the critical points of the two phase transitions for N>4 is established and the critical index \nu\ is computed. For N=7, 17 the critical points are located by Monte Carlo simulations and some of the corresponding critical indices are determined. The behavior of the helicity modulus is studied for N=5, 7, 17. Using these and other available Monte Carlo data we discuss the scaling of the critical points with N and some other open theoretical problems.Comment: 19 pages, 8 figures, 10 tables; version to appear on Phys. Rev.

Ghost-gluon coupling, power corrections and ΛMSˉ\Lambda_{\bar{MS}} from twisted-mass lattice QCD at Nf=2N_f=2

A non-perturbative calculation of the ghost-gluon running QCD coupling constant is performed using $N_f=2$ twisted-mass dynamical fermions. The extraction of $\Lambda_{\bar{MS}}$ in the chiral limit reveals the presence of a non-perturbative OPE contribution that is assumed to be dominated by a dimension-two \VEV{A^2} condensate. In this contest a novel method for calibrating the lattice spacing in lattice simulations is presented.Comment: 7 pages, 4 figures, XXVIII International Symposium on Lattice Field Theory 201

Critical behavior of the compact 3d U(1) gauge theory on isotropic lattices

We report on the computation of the critical point of the deconfinement phase transition, critical indices and the string tension in the compact three dimensional U(1) lattice gauge theory at finite temperatures. The critical indices govern the behavior across the deconfinement phase transition in the pure gauge U(1) model and are generally expected to coincide with the critical indices of the two-dimensional XY model. We studied numerically the U(1) model for N_t=8 on lattices with spatial extension ranging from L=32 to L=256. Our determination of the infinite volume critical point on the lattice with N_t=8 differs substantially from the pseudo-critical coupling at L=32, found earlier in the literature and implicitly assumed as the onset value of the deconfined phase. The critical index $\nu$ computed from the scaling of the pseudo-critical couplings with the extension of the spatial lattice agrees well with the XY value $\nu$=1/2. On the other hand, the index $\eta$ shows large deviation from the expected universal value. The possible reasons of such behavior are discussed in details.Comment: 15 pages, 7 figures; version accepted for publication on J. Stat. Mech

Critical behavior of the compact 3d U(1) theory in the limit of zero spatial coupling

Critical properties of the compact three-dimensional U(1) lattice gauge theory are explored at finite temperatures on an asymmetric lattice. For vanishing value of the spatial gauge coupling one obtains an effective two-dimensional spin model which describes the interaction between Polyakov loops. We study numerically the effective spin model for N_t=1,4,8 on lattices with spatial extension ranging from L=64 to L=256. Our results indicate that the finite-temperature U(1) lattice gauge theory belongs to the universality class of the two-dimensional XY model, thus supporting the Svetitsky-Yaffe conjecture.Comment: 17 pages, 5 figures; two references added, a few comments included, title changed; version to appear on J. Stat. Mec

Ghost-gluon coupling, power corrections and ΛMS‾\Lambda_{\overline {\rm MS}} from twisted-mass lattice QCD at Nf=2

We present results concerning the non-perturbative evaluation of the ghost-gluon running QCD coupling constant from $N_f=2$ twisted-mass lattice calculations. A novel method for calibrating the lattice spacing, independent of the string tension and hadron spectrum is presented with results in agreement with previous estimates. The value of $\Lambda_{\overline{MS}}$ is computed from the running of the QCD coupling only after extrapolating to zero dynamical quark mass and after removing a non-perturbative OPE contribution that is assumed to be dominated by the dimension-two \VEV{A^2} gluon condensate. The effect due to the dynamical quark mass in the determination of \Lams is discussed.Comment: 33 pages, 6 fig

Phase transitions in strongly coupled 3d Z(N) lattice gauge theories at finite temperature

We perform an analytical and numerical study of the phase transitions in three-dimensional Z(N) lattice gauge theories at finite temperature for N>4 exploiting equivalence of these models with a generalized version of the two-dimensional vector Potts models in the limit of vanishing spatial coupling. In this limit the Polyakov loops play the role of Z(N) spins. The effective couplings of these two-dimensional spin models are calculated explicitly. It is argued that the effective spin models have two phase transitions of BKT type. This is confirmed by large-scale Monte Carlo simulations. Using a cluster algorithm we locate the position of the critical points and study the critical behavior across both phase transitions in details. In particular, we determine various critical indices, compute the helicity modulus, the average action and the specific heat. A scaling formula for the critical points with N is proposed.Comment: 28 pages, 12 figures, 12 tables; version to appear on Phys. Rev.