Palindromic 3-stage splitting integrators, a roadmap

The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be easily incorporated into software that now uses the Strang/Verlet integrator. We study in detail the two-parameter family of palindromic, three-stage splitting formulas and identify choices of parameters that may outperform the Strang/Verlet method. One of these choices leads to a method of effective order four suitable to integrate in time some partial differential equations. Other choices may be seen as perturbations of the Strang method that increase efficiency in molecular dynamics simulations and in Hybrid Monte Carlo sampling.Comment: 20 pages, 8 figures, 2 table

Towards the lattice study of M-theory

We propose the Wilson discretization of the supersymmetric Yang-Mills Quantum Mechanics as a lattice version of the matrix model of M-theory. An SU(2) model is studied numerically in the quenched approximation for D=4. A clear signal for the existence of two different phases is found and the continuum pseudocritical temperature is determined. We have also extracted the continuum limit of the total size of the system in both phases and for different temperatures.Comment: Lattice 2000 (Gravity and Matrix Models

Study of the order of the phase transition in pure U(1) gauge theory with Villain action

We address the question of the order of the deconfinement phase transition of four dimensional U(1) lattice gauge theory. Simulations of the Z-gauge theory dual to the Villain action on toroidal lattices up to lattice sizes of 28^4 give results consistent with both, a vanishing and a nonvanishing discontinuity in the thermodynamic limit. A decision on the order of the phase transition requires still larger lattice sizes.Comment: LATTICE98(gauge), 3 pages, 2 figure