Lattice Landau gauge and other related lattice gauge fixing schemes are known to violate spectral positivity. The most direct sign of the violation is the rise of the effective mass as a function of distance. The origin of this phenomenon lies in the quenched character of the auxiliary field g used to implement lattice gauge fixing, and is similar to quenched QCD in this respect. This is best s...

We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label equivalence classes which allow a rearrangement of the sum over paths. The basic combinatorial quantities of this construction are given. These formulas are usefu...

Given a rational lattice and suitable set of linear transformations, we construct a cousin lattice. Sufficient conditions are given for integrality, evenness and unimodularity. When the input is a Barnes-Wall lattice, we get multi-parameter series of cousins. There is a subseries consisting of unimodular lattices which have ranks 2d−1 ± 2d−k−1, for odd integers d ≥ 3 and integers k = 1, 2, · · ...

The different techniques available for the accurate measurement of lattice fringe spacings are discussed and their relative merit under different circumstances assessed. The relationship between the lattice fringe spacing and the lattice parameter is further examined for both uniform and chemically inhomogeneous material. The techniques described were also applied to an investigation of carbon ...

On the basis of the recently developed lattice formulation of supersymmetric theories which keeps a part of the supersymmetry, we propose a method of observing dynamical SUSY breaking with lattice simulation. We use Hamiltonian as an order parameter and measure the ground state energy as a zero temperature limit of the finite temperature simulation. Our method provides a way of obtaining a phys...

We present a set of exactly solvable fermionic spin-S Ising model on a square-type lattice including a quartic interaction term in the Hamiltonian, using an auxiliary mixed fermionic spin-(S,1/2) square-type lattice with only first nearest-neighbor interaction. The particular properties of the mixed lattice, associated to the fermionic mixed spin-(S,1/2), allow us to map this system either into...

The problem of color confinement in lattice Landau gauge QCD is briefly reviewed in the light of Kugo-Ojima criterion and Gribov-Zwanziger theory. The infrared properties of the Landau gauge QCD is studied by the measurement of the gluon propagator, ghost propagator, Kugo-Ojima parameter and the running coupling via β = 6.0, 16, 24, 32 and β = 6.4, 32, 48 lattice simulation. The data are analyz...

To base the kilogram definition on the atomic mass of the Si atom, the present relative uncertainty of the Si lattice parameter must lowered to 3 × 10. To achieve this goal, a new experimental apparatus capable of a centimetre measurement-baseline has been made at the INRIM. The comparison between the determinations of the lattice parameter of crystals MO*4 of INRIM and WASO 4.2a of PTB is inte...

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniv...

Energy transport control in low dimensional nanoscale systems has attracted much attention in recent years. In this paper, we investigate the energy transport properties of the Frenkel-Kontorova lattice subject to a periodic driving force, in particular, the resonance behavior of the energy current by varying the external driving frequency. It is discovered that, in certain parameter ranges, mu...