Classification of Minimally Doubled Fermions

We propose a method to control the number of species of lattice fermions which yields new classes of minimally doubled lattice fermions. We show it is possible to control the number of species by handling $O(a)$ Wilson-term-like corrections in fermion actions, which we will term ``Twisted-ordering Method". Using this method we obtain new minimally doubled actions with one exact chiral symmetry and exact locality. We classify the known minimally doubled fermions into two types based on the locations of the propagator poles in the Brillouin zone.Comment: 23 pages, 6 figures; version accepted in Phys.Rev.

End states, ladder compounds, and domain wall fermions

A magnetic field applied to a cross linked ladder compound can generate isolated electronic states bound to the ends of the chain. After exploring the interference phenomena responsible, I discuss a connection to the domain wall approach to chiral fermions in lattice gauge theory. The robust nature of the states under small variations of the bond strengths is tied to chiral symmetry and the multiplicative renormalization of fermion masses.Comment: 10 pages, 4 figures; final version for Phys. Rev. Let

Chiral Symmetry Versus the Lattice

After mentioning some of the difficulties arising in lattice gauge theory from chiral symmetry, I discuss one of the recent attempts to resolve these issues using fermionic surface states in an extra space-time dimension. This picture can be understood in terms of end states on a simple ladder molecule.Comment: Talk at the meeting "Computer simulations studies in condensed matter physics XIV" Athens, Georgia, Feb. 19-24, 2001. 14 page

Low temperature expansion for the 3-d Ising Model

We compute the weak coupling expansion for the energy of the three dimensional Ising model through 48 excited bonds. We also compute the magnetization through 40 excited bonds. This was achieved via a recursive enumeration of states of fixed energy on a set of finite lattices. We use a linear combination of lattices with a generalization of helical boundary conditions to eliminate finite volume effects.Comment: 10 pages, IASSNS-HEP-92/42, BNL-4767

The Method of Recursive Counting: Can One Go Further?

After a short review of the Method of Recursive Counting we introduce a general algebraic description of recursive lattice building. This provides a rigorous framework for discussion of method's limitations.Comment: 3 pages, compressed uuencoded postscript file; Talk presented at the Lattice '93 conference in Dallas, BNL-4978

Quantum Phase Transition in a Graphene Model

We present results for the equation of state of a graphene-like model in an effort to understand the properties of its quantum phase transition. The N_f fermion species interact through a three dimensional instantaneous Coulomb potential. Since there are no reliable analytical tools that work for all values of N_f and the coupling constant g, we rely on Monte Carlo simulations to calculate the critical properties of the model near the phase transition. We consider the four-component formulation for the fermion fields, which arises naturally as the continuum limit of the staggered fermion construction in (2+1) dimensions. In the limit of infinitely strong Coulomb interaction, the system undergoes a quantum phase transition at a critical number of fermion species N_fc ~ 4.7. We also calculate the values of the critical exponents at the quantum phase transition.Comment: 4 pages, 3 figures, presented at the 25th international conference on Low Temperature Physics, 6-13 August 2008, Amsterda

Deconfinement in Yang-Mills: a conjecture for a general gauge Lie group G

Svetitsky and Yaffe have argued that -- if the deconfinement phase transition of a (d+1)-dimensional Yang-Mills theory with gauge group G is second order -- it should be in the universality class of a d-dimensional scalar model symmetric under the center C(G) of G. These arguments have been investigated numerically only considering Yang-Mills theory with gauge symmetry in the G=SU(N) branch, where C(G)=Z(N). The symplectic groups Sp(N) provide another extension of SU(2)=Sp(1) to general N and they all have the same center Z(2). Hence, in contrast to the SU(N) case, Sp(N) Yang-Mills theory allows to study the relevance of the group size on the order of the deconfinement phase transition keeping the available universality class fixed. Using lattice simulations, we present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories both in (2+1)d and (3+1)d. We then make a conjecture on the order of the deconfinement phase transition in Yang-Mills theories with general Lie groups SU(N), SO(N), Sp(N) and with exceptional groups G(2), F(4), E(6), E(7), E(8). Numerical results for G(2) Yang-Mills theory at finite temperature in (3+1)d are also presented.Comment: Invited talk at the International Workshop "QCD DOWN UNDER", Adelaide, Australia, 10-19 Mar 2004. 6 pages, 6 figure

Improved Superlinks for Higher Spin Operators

Traditional smearing or blocking techniques serve well to increase the overlap of operators onto physical states but allow for links orientated only along lattice axes. Recent attempts to construct more general propagators have shown promise at resolving the higher spin states but still rely on iterative smearing. We present a new method of superlink construction which creates meared links from (sparse) matrix multiplications, allowing for gluonic propagation in arbitrary directions. As an application and example, we compute the positive-parity, even-spin glueball spectrum up to spin 6 for pure gauge SU(2) at beta = 6, L = 16, in D = 2+1 dimensions.Comment: 27 pages, 10 tables, 8 figures, uses RevTex4, minor corrections and further development, reunitarized superlinks, as accepted by PR

Properties of the vector meson nonet at large N_c beyond the chiral limit

Masses and especially coupling constants of the vector meson nonet are determined in the large-N_c limit, but beyond the chiral limit taking into account terms up to quadratic order in the Goldstone boson masses. With two input parameters five coupling constants for hadronic and dilepton decays are determined which agree very well with the experimental results. The obtained parameters are also used to calculate the pion and kaon decay constant in the large-N_c limit. A consistent picture is only obtained, if the correct assignment of the N_c-dependence of the electromagnetic charges of the quarks is taken into account.Comment: 12 pages, strongly rewritten, more focussed on the central issu