New Algorithm of the Finite Lattice Method for the High-temperature Expansion of the Ising Model in Three Dimensions

We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous series of 26th order to 46th order in the inverse temperature. The obtained series give the estimate of the critical exponent for the specific heat in high precision.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Letter

Numerical results from large N reduced QCD_2

Some results in QCD_2 at large N are presented using the reduced model on the lattice. Overlap fermions are used to compute meson propagators.Comment: 3 pages, contribution to Lattice 2002, Bosto

Custodial Symmetry and the Triviality Bound on the Higgs Mass

The triviality of the scalar sector of the standard one-doublet Higgs model implies that it is only an effective low-energy theory valid below some cut-off scale $\Lambda$. In this note we show that the experimental constraint on the amount of custodial symmetry violation, $|\Delta \rho_* | = \alpha |T | \le 0.4\%$, implies that the scale $\Lambda$ must be greater than of order 7.5 TeV. For theories defined about the infrared-stable Gaussian fixed-point, we estimate that this lower bound on $\Lambda$ yields an upper bound of approximately 550 GeV on the Higgs boson's mass, independent of the regulator chosen to define the theory. We also show that some regulator schemes, such as higher-derivative regulators, used to define the theory about a different fixed-point are particularly dangerous because an infinite number of custodial-isospin-violating operators become relevant.Comment: 2 references added; 8 pages, 3 embedded Postscript figures, LaTeX, full postscript version also available at http://smyrd.bu.edu/htfigs/htfigs.htm

Low-Temperature Series for Ising Model by Finite-Lattice Method

We have calculated the low-temperature series for the second moment of the correlation function in $d=3$ Ising model to order $u^{26}$ and for the free energy of Absolute Value Solid-on-Solid (ASOS) model to order $u^{23}$, using the finite-lattice method.Comment: 3pages, latex, no figures, talk given at LATTICE'94, to appear in the proceeding

Large-q expansion of the energy and magnetization cumulants for the two-dimensional q-state Potts model

We have calculated the large-q expansion for the energy cumulants and the magnetization cumulants at the phase transition point in the two-dimensional q-state Potts model to the 21st or 23rd order in $1/\sqrt{q}$ using the finite lattice method. The obtained series allow us to give very precise estimates of the cumulants for $q>4$ on the first order transition point. The result confirms us the correctness of the conjecture by Bhattacharya et al. on the asymptotic behavior not only of the energy cumulants but also of the magnetization cumulants for $q \to 4_+$.Comment: 36 pages, LaTeX, 20 postscript figures, to appear in Nuclear Physics

Phases of three dimensional large N QCD on a continuum torus

It is established by numerical means that continuum large N QCD defined on a three dimensional torus can exist in four different phases. They are (i) confined phase; (ii) deconfined phase; (iii) small box at zero temperature and (iv) small box at high temperatures.Comment: 11 pages, 6 figures, 1 tabl

Fast vectorized algorithm for the Monte Carlo Simulation of the Random Field Ising Model

An algoritm for the simulation of the 3--dimensional random field Ising model with a binary distribution of the random fields is presented. It uses multi-spin coding and simulates 64 physically different systems simultaneously. On one processor of a Cray YMP it reaches a speed of 184 Million spin updates per second. For smaller field strength we present a version of the algorithm that can perform 242 Million spin updates per second on the same machine.Comment: 13 pp., HLRZ 53/9

Low-Temperature Series for the Correlation Length in d=3d=3 Ising Model

We extend low-temperature series for the second moment of the correlation function in $d=3$ simple-cubic Ising model from $u^{15}$ to $u^{26}$ using finite-lattice method, and combining with the series for the susceptibility we obtain the low-temperature series for the second-moment correlation length to $u^{23}$. An analysis of the obtained series by inhomogeneous differential approximants gives critical exponents $2\nu^{\prime} + \gamma^{\prime} \approx 2.55$ and $2\nu^{\prime} \approx 1.27$.Comment: 13 pages + 5 uuencoded epsf figures in Latex, OPCT-94-

Large N reduction in the continuum three dimensional Yang-Mills theory

Numerical and theoretical evidence leads us to propose the following: Three dimensional Euclidean Yang-Mills theory in the planar limit undergoes a phase transition on a torus of side $l=l_c$. For $l>l_c$ the planar limit is $l$-independent, as expected of a non-interacting string theory. We expect the situation in four dimensions to be similar.Comment: 4 pages, latex file, two figures, version to appear in Phys. Rev. Let

New algorithm of the high-temperature expansion for the Ising model in three dimensions

New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of the finite lattice method but also to the standard graphical method. It is applied to extend the high-temperature series of the simple cubic Ising model from beta^{26} to beta^{46} for the free energy and from beta^{25} to beta^{32} for the magnetic susceptibility.Comment: 3 pages, Lattice2002(spin