Critical couplings and string tensions via lattice matching of RG decimations

We calculate critical couplings and string tensions in SU(2) and SU(3) pure lattice gauge theory by a simple and inexpensive technique of two-lattice matching of RG block transformations. The transformations are potential moving decimations generating plaquette actions with large number of group characters and exhibit rapid approach to a unique renormalized trajectory. Fixing the critical coupling $\beta_c(N_\tau)$ at one value of temporal lattice length $N_\tau$ by MC simulation, the critical couplings for any other value of $N_\tau$ are then obtained by lattice matching of the block decimations. We obtain $\beta_c(N_\tau)$ values over the range $N_\tau = 3 - 32$ and find agreement with MC simulation results to within a few percent in all cases. A similar procedure allows the calculation of string tensions with similarly good agreement with MC data.Comment: 12 pages, Latex, 1 figur

Quark Confinement and the Renormalization Group

Recent approaches to quark confinement are reviewed, with an emphasis on their connection to renormalization group methods. Basic concepts related to confinement are introduced: the string tension, Wilson loops and Polyakov lines, string breaking, string tension scaling laws, center symmetry breaking, and the deconfinement transition at non-zero temperature. Current topics discussed include confinement on $R^3\times S^1$, the real-space renormalization group, the functional renormalization group, and the Schwinger-Dyson equation approach to confinement.Comment: 22 pages; report from the INT Workshop "New applications of the renormalization group in nuclear, particle, and condensed matter physics", held February 22-26 201

Mixed Model of Induced QCD

The problems with the $Z_N$ symmetry breaking in the induced QCD are analyzed. We compute the Wilson loops in the strong coupling phase, but we do not find the $Z_N$ symmetry breaking, for arbitrary potential. We suggest to bypass this problem by adding to the model a heavy fermion field in a fundamental representation of $SU(N)$. Remarkably, the model still can be solved exactly by the Rieman-Hilbert method, for arbitrary number $N_f$ of flavors. At $N_f \ll N \rightarrow \infty$ there is a new regime, with two vacuum densities. The $Z_N$ symmetry breaking density satisfies the linear integral equation, with the kernel, depending upon the old density. The symmetry breaking requires certain eigenvalue condition, which takes some extra parameter adjustment of the scalar potential.Comment: 14 pages, Latex, no figures, ( after final debugging

1/N Expansion and Particle Spectrum in Induced QCD

We study the 1/N expansion in the recently proposed model of the lattice gauge theory induced by heavy scalar field in adjoint representation. In the first approximation the fluctuations of the density of eigenvalues of the scalar field are Gaussian, so that the scalar glueball spectrum is defined from the corresponding linear wave equation

Bose Condensation and ZNZ_N Symmetry Breaking in the Mixed Model of Induced QCD

The mixed model of the large $N$ induced QCD, with $N_f \ll N$ flavors of heavy fermions in fundamental representation, is solved in the local limit. The $Z_N$ symmetry is broken spontaneously in the large $N$ limit, evading the Elitzur "no-go" theorem. As a result of this symmetry breaking, there is the Bose condensate of the eigenvalues of the scalar field, proportional to $\frac{N_f}{N}$. This condensate leads to the mass unit, which goes to zero as fractional power of $\frac{N_f}{N}$, thus defining the new kind of the local limit of this lattice theory. There is a strong coupling region below this mass scale, which revives the hopes of induction of realistic QCD.Comment: 16 pages, Latex, no figures, PUPT-134

Two-dimensional Born-Infeld gauge theory: spectrum, string picture and large-N phase transition

We analyze U(N) Born-Infeld gauge theory in two spacetime dimensions. We derive the exact energy spectrum on the circle and show that it reduces to N relativistic fermions on a dual space. This contrasts to the Yang-Mills case that reduces to nonrelativistic fermions. The theory admits a string theory interpretation, analogous to the one for ordinary Yang-Mills, but with higher order string interactions. We also demonstrate that the partition function on the sphere exhibits a large-N phase transition in the area and calculate the critical area. The limit in which the dimensionless coupling of the theory goes to zero corresponds to massless fermions, admits a perturbatively exact free string interpretation and exhibits no phase transition.Comment: 19 page

Finite-temperature phase diagram of nonmagnetic impurities in high-temperature superconductors using a d=3 tJ model with quenched disorder

We study a quenched disordered d=3 tJ Hamiltonian with static vacancies as a model of nonmagnetic impurities in high-Tc materials. Using a position-space renormalization-group approach, we calculate the evolution of the finite-temperature phase diagram with impurity concentration p, and find several features with close experimental parallels: away from half-filling we see the rapid destruction of a spin-singlet phase (analogous to the superconducting phase in cuprates) which is eliminated for p > 0.05; in the same region for these dilute impurity concentrations we observe an enhancement of antiferromagnetism. The antiferromagnetic phase near half-filling is robust against impurity addition, and disappears only for p > 0.40.Comment: 5 pages, 4 figures; replaced with published versio

High-Precision Thermodynamic and Critical Properties from Tensor Renormalization-Group Flows

The recently developed tensor renormalization-group (TRG) method provides a highly precise technique for deriving thermodynamic and critical properties of lattice Hamiltonians. The TRG is a local coarse-graining transformation, with the elements of the tensor at each lattice site playing the part of the interactions that undergo the renormalization-group flows. These tensor flows are directly related to the phase diagram structure of the infinite system, with each phase flowing to a distinct surface of fixed points. Fixed-point analysis and summation along the flows give the critical exponents, as well as thermodynamic functions along the entire temperature range. Thus, for the ferromagnetic triangular lattice Ising model, the free energy is calculated to better than 10^-5 along the entire temperature range. Unlike previous position-space renormalization-group methods, the truncation (of the tensor index range D) in this general method converges under straightforward and systematic improvements. Our best results are easily obtained with D = 24, corresponding to 4624-dimensional renormalization-group flows.Comment: 6 pages, 5 figure