Search Results (72 total)

A recent criticism of the proof of the failure of the rooting procedure with staggered fermions is shown to be incorrect.

Using effective Lagrangian arguments, I explore the qualitative behavior expected at finite temperature for two-flavor lattice QCD formulated with Wilson fermions and a twisted mass term. A rather rich phase structure is predicted, exhibiting Aoki’s parity violating phase along with a deconfinement region forming a conical structure in the space of coupling, hopping parameter, and twisted mass variables.

The admissibility condition usually used to define the topological charge in lattice gauge theory is incompatible with a positive transfer matrix.

Some time ago Dashen [Phys. Rev. D 3, 1879 (1971)] pointed out that spontaneous CP violation can occur in the strong interactions. I show how a simple effective Lagrangian exposes the remarkably large domain of quark mass parameters for which this occurs. I close with some warnings for lattice simulations.

It has long been known that no physical singularity is encountered as up-quark mass is adjusted from small positive to negative values as long as all other quarks remain massive. This is tied to an additive ambiguity in the definition of the quark mass. This calls into question the acceptability of attempts to solve the strong CP problem via a vanishing mass for the lightest quark.

This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, the author discusses how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP-violating parameter Θ. One particularly elegant scheme for exploring this physics on the lattice is presented in some detail. This uses an auxiliary extra space-time dimension, with the physical world being a four-dimensional interface.

This article is a pedagogical exploration of the nonperturbative issues entwining lattice gauge theory, anomalies, and chiral symmetry. After briefly reviewing the importance of chiral symmetry in particle physics, the author discusses how anomalies complicate lattice formulations. Considerable information can be deduced from effective chiral Lagrangians, helping interpret the expectations for lattice models and elucidating the role of the CP-violating parameter Θ. One particularly elegant scheme for exploring this physics on the lattice is presented in some detail. This uses an auxiliary extra space-time dimension, with the physical world being a four-dimensional interface.

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.

I discuss a simple numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow exponentially with the interaction range and the transverse size of the system. Low dimensional systems with 1000 Grassmann variables can be evaluated on a workstation. The technique is illustrated with a spinless fermion hopping along a one dimensional chain.

Coupling gauge fields to the chiral currents from an effective Lagrangian for pseudoscalar mesons naturally gives rise to a species doubling phenomenon similar to that seen with fermionic fields in lattice gauge theory.

I discuss the global structure of the strongly interacting gauge theory of quarks and gluons as a function of the quark masses and the CP-violating parameter θ. I concentration on whether a first order phase transition occurs at θ=π. I show why this is expected when multiple flavors have a small degenerate mass. This transition can be removed by sufficient flavor breaking. I speculate on the implications of this structure for Wilson’s lattice fermions.

In a Hamiltonian formalism we study chiral symmetry for lattice fermions formulated in terms of Shockley surface states bound to a wall in an extra spatial dimension. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. We illustrate the chiral anomaly as a flow of states in this extra dimension. We discuss two alternatives for extending the picture to a chiral coupling of gauge fields to such fermions: one with a small explicit breaking of gauge symmetry and one with heavy mirror fermions.

We compute high-temperature expansions of the three-dimensional Ising model using a recursive transfer-matrix algorithm and extend the expansion of the free energy to 24th order. Using inhomogeneous-differential Padé and ratio methods, we extract the critical exponent of the specific heat to be α=0.104(4).

We discuss the use of recursive enumeration schemes to obtain low- and high-temperature series expansions for discrete statistical systems. Using linear combinations of generalized helical lattices, the method is competitive with diagrammatic approaches and is easily generalizable. We illustrate the approach using Ising and Potts models. We present low-temperature series results in up to five dimensions and high-temperature series in three dimensions. The method is general and can be applied to any discrete model.

On simple-cubic lattices, we compute low-temperature series expansions for the energy, magnetization, and susceptibility of the three-state Potts model in D=2 and D=3 to 45 and 39 excited bonds, respectively, and the eight-state Potts model in D=2 to 25 excited bonds. We use a recursive procedure that enumerates states explicitly. We analyze the series with Dlog Padé analysis and inhomogeneous differential approximants.

On simple cubic lattices, we compute the low-temperature expansion for the energy of the Ising model through 50 excited bonds in three dimensions and 44 excited bonds in four dimensions. We also give the magnetization through 42 excited bonds. Our method is a recursive enumeration of states with given energies on a set of finite lattices with generalized helical boundary conditions. A linear combination of such lattices cancels finite volume effects.

I propose a numerical simulation algorithm for statistical systems which combines a microcanonical transfer of energy with global changes in clusters of spins. The advantages of the cluster approach near a critical point augment the speed increases associated with multispin coding in the microcanonical approach. The method also provides a limited ability to tune the average cluster size.

I explore a recursive enumeration of world-line diagrams as a numerical approach to simulating many-fermion lattice systems. Signs from fermion exchange are treated exactly. In addition, all values of the coupling constants are treated simultaneously. The method is computationally fast, although large-memory requirements restrict it to small spatial systems.

A modified Wilson action with an additional chemical potential for the number of "negative plaquettes" is used to study the role of Z₂ artifacts in SU(2) lattice gauge theory and their possible influence on large-scale physics. The phase diagram of the model with modified action is studied. We show that large-scale objects, e.g., Wilson loops and their ratios, can be strongly influenced by lattice artifacts.

I present a simple numerical technique for evaluating the low-temperature expansion for discrete statistical systems. I begin with a recursive procedure on finite lattices to count the states of a given energy. Comparing these numbers on different lattice sizes, I extract coefficients for the infinite-volume series. I test the method with the three-dimensional Ising model, obtaining the expansion of the average energy through terms involving 34 excited bonds.

We present a simple recursive iteration of the leapfrog discretization of Newton’s equations which leads to a removal of the finite-step-size error to any desired order. This is done in a manner that preserves phase-space areas and reversibility, as required for use in the hybrid Monte Carlo method for simulating fermionic fields. The resulting asymptotic volume dependence is exp[(lnV)^1/2]. We test the scheme on the (2+1)-dimensional Hubbard model.

We introduce a general updating scheme for the simulation of physical systems defined on unitary groups, which eliminates the systematic errors due to inexact exponentiation of algebra elements. The essence is to work directly with group elements for the stochastic noise. Particular cases of the scheme include the algorithm of Metropolis et al., overrelaxation algorithms, and globally corrected Langevin and hybrid algorithms. The latter are studied numerically for the case of SU(3) theory.

I discuss algorithms for simulating many-fermion systems via global updatings of auxiliary fields followed by an accept-reject stage which eliminates finite-step-size errors. When the system size is larger than the correlation length, these procedures should require computer time growing only slightly faster than linearly with the system volume V. A corrected Langevin scheme should asymptotically display a V^4/3 behavior, while the hybrid Monte Carlo scheme can behave as V^5/4. I present some tests of the latter algorithm on a simple model of interacting electrons on a two-dimensional lattice.

I study a simple variation of the algorithm of Metropolis et al. for simulating statistical systems. The trial changes in any given variable are taken from a region of phase space far from the old value but involving only small changes in energy. This results in correlation times which are short compared to the usual applications of the algorithm of Metropolis et al. Tests with SU(2) and SU(3) lattice gauge theories indicate substantial possible savings in computation time relative to standard approaches.

The transfer-matrix formalism for relating Hamiltonian quantum mechanics and Euclidean path integrals is discussed in the context of fermionic fields. Particular emphasis is placed on the extra fermionic species encountered with the naive discretization of time. When both particles and antiparticles are present, the Wilson projection-operator formalism arises naturally for the temporal coordinate. We discuss in detail how the Hilbert space must be enlarged to remove these projections.