7,787 research outputs found

    A cluster algorithm for Lattice Gauge Theories

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    A new algorithm for simulating compact U(1) lattice gauge theory in three dimensions is presented which is based on global changes in the configuration space. We show that this algorithm provides an effective way to extract partition functions at given external flux. As an application, we study numerically the finite temperature deconfinement phase transition.Comment: 4 pages, 2 figures. Talk given at the Conference on Computational Physics, Genova, Italy, Sept. 200

    Chiral Limit of Strongly Coupled Lattice Gauge Theories

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    We construct a new and efficient cluster algorithm for updating strongly coupled U(N) lattice gauge theories with staggered fermions in the chiral limit. The algorithm uses the constrained monomer-dimer representation of the theory and should also be of interest to researchers working on other models with similar constraints. Using the new algorithm we address questions related to the chiral limit of strongly coupled U(N) gauge theories beyond the mean field approximation. We show that the infinite volume chiral condensate is non-zero in three and four dimensions. However, on a square lattice of size LL we find xL2η\sum_x \sim L^{2-\eta} for large LL where η=0.420(3)/N+0.078(4)/N2\eta = 0.420(3)/N + 0.078(4)/N^2. These results differ from an earlier conclusion obtained using a different algorithm. Here we argue that the earlier calculations were misleading due to uncontrolled autocorrelation times encountered by the previous algorithm.Comment: 36 Pages, 9 figures, aps revtex forma

    D-Theory: Field Theory via Dimensional Reduction of Discrete Variables

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    A new non-perturbative approach to quantum field theory --- D-theory --- is proposed, in which continuous classical fields are replaced by discrete quantized variables which undergo dimensional reduction. The 2-d classical O(3) model emerges from the (2+1)-d quantum Heisenberg model formulated in terms of quantum spins. Dimensional reduction is demonstrated explicitly by simulating correlation lengths up to 350,000 lattice spacings using a loop cluster algorithm. In the framework of D-theory, gauge theories are formulated in terms of quantum links --- the gauge analogs of quantum spins. Quantum links are parallel transporter matrices whose elements are non-commuting operators. They can be expressed as bilinears of anticommuting fermion constituents. In quantum link models dimensional reduction to four dimensions occurs, due to the presence of a 5-d Coulomb phase, whose existence is confirmed by detailed simulations using standard lattice gauge theory. Using Shamir's variant of Kaplan's fermion proposal, in quantum link QCD quarks appear as edge states of a 5-d slab. This naturally protects their chiral symmetries without fine-tuning. The first efficient cluster algorithm for a gauge theory with a continuous gauge group is formulated for the U(1) quantum link model. Improved estimators for Wilson loops are constructed, and dimensional reduction to ordinary lattice QED is verified numerically.Comment: 15 pages, LaTeX, including 9 encapsulated postscript figures. Contribution to Lattice 97 by 5 authors, to appear in Nuclear Physics B (Proceeding Supplements). Requires psfig.tex and espcrc2.st

    Kosterlitz Thouless Universality in Dimer Models

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    Using the monomer-dimer representation of strongly coupled U(N) lattice gauge theories with staggered fermions, we study finite temperature chiral phase transitions in (2+1) dimensions. A new cluster algorithm allows us to compute monomer-monomer and dimer-dimer correlations at zero monomer density (chiral limit) accurately on large lattices. This makes it possible to show convincingly, for the first time, that these models undergo a finite temperature phase transition which belongs to the Kosterlitz-Thouless universality class. We find that this universality class is unaffected even in the large N limit. This shows that the mean field analysis often used in this limit breaks down in the critical region.Comment: 4 pages, 4 figure

    Progress in Lattice Field Theory Algorithms

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    I present a summary of recent algorithmic developments for lattice field theories. In particular I give a pedagogical introduction to the new Multicanonical algorithm, and discuss the relation between the Hybrid Overrelaxation and Hybrid Monte Carlo algorithms. I also attempt to clarify the role of the dynamical critical exponent z and its connection with `computational cost.' [Includes four PostScript figures]Comment: 27 page

    Quantum Link Models: A Discrete Approach to Gauge Theories

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    We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed matter physics. When formulated with a fifth Euclidean dimension, universality arguments suggest that dimensional reduction to four dimensions occurs. Hence, quantum link models are also reformulations of ordinary quantum field theories and are applicable to particle physics, for example to QCD. The configuration space of quantum link models is discrete and hence their numerical treatment should be simpler than that of ordinary lattice gauge theories with a continuous configuration space.Comment: 18 pages, Latex, no figures, final version to appear in Nuclear Physics B, references to earlier work by Horn, Orland and Rohrlich include
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