1,258 research outputs found

### Monte Carlo simulations and field transformation: the scalar case

We describe a new method in lattice field theory to compute observables at
various values of the parameters lambda_i in the action S[phi,lambda_i].
Firstly one performs a single simulation of a ``reference action'' S[phi^r,
lambda_i^r] with fixed lambda_i^r. Then the phi^r-configurations are
transformed into those of a field phi distributed according to S[phi,lambda_i],
apart from a ``remainder action'' which enters as a \break weight. In this way
we measure the observables at values of lambda_i different from lambda_i^r. We
study the performance of the algorithm in the case of the simplest
renormalizable model, namely the phi^4 scalar theory on a four dimensional
lattice and compare the method with the ``histogram'' technique of which it is
a generalization.Comment: Latex, 23 pgs, 8 eps-figures include

### Finite size effects at phase transition in compact U(1) gauge theory

We present and discuss the results of a Monte-Carlo simulation of the phase
transition in pure compact U(1) lattice gauge theory with Wilson action on a
hypercubic lattice with periodic boundary conditions. The statistics are large
enough to make a thorough analysis of the size dependence of the gap. In
particular we find a non-zero latent heat in the infinite volume limit. We also
find that the critical exponents $\nu$ and $\alpha$ are consistent with the
hyperscaling relation but confirm that the critical behavior is different from
a conventional first-order transition.Comment: Talk presented at Lattice '97; 3 pages, Latex fil

### High precision single-cluster Monte Carlo measurement of the critical exponents of the classical 3D Heisenberg model

We report measurements of the critical exponents of the classical
three-dimensional Heisenberg model on simple cubic lattices of size $L^3$ with
$L$ = 12, 16, 20, 24, 32, 40, and 48. The data was obtained from a few long
single-cluster Monte Carlo simulations near the phase transition. We compute
high precision estimates of the critical coupling $K_c$, Binder's parameter
$U^* and the critical exponents$\nu,\beta / \nu, \eta$, and$\alpha / \nu$,
using extensively histogram reweighting and optimization techniques that allow
us to keep control over the statistical errors. Measurements of the
autocorrelation time show the expected reduction of critical slowing down at
the phase transition as compared to local update algorithms. This allows
simulations on significantly larger lattices than in previous studies and
consequently a better control over systematic errors in finite-size scaling
analyses.Comment: 4 pages, (contribution to the Lattice92 proceedings) 1 postscript
file as uufile included. Preprints FUB-HEP 21/92 and HLRZ 89/92. (note: first
version arrived incomplete due to mailer problems

### Critical behaviour of SU(2) lattice gauge theory. A complete analysis with the $\chi^2$-method

We determine the critical point and the ratios $\beta/\nu$ and $\gamma/\nu$
of critical exponents of the deconfinement transition in $SU(2)$ gauge theory
by applying the $\chi^2$-method to Monte Carlo data of the modulus and the
square of the Polyakov loop. With the same technique we find from the Binder
cumulant $g_r$ its universal value at the critical point in the thermodynamical
limit to $-1.403(16)$ and for the next-to-leading exponent $\omega=1\pm0.1$.
From the derivatives of the Polyakov loop dependent quantities we estimate then
$1/\nu$. The result from the derivative of $g_r$ is $1/\nu=0.63\pm0.01$, in
complete agreement with that of the $3d$ Ising model.Comment: 11 pages, 3 Postscript figures, uses Plain Te

### Non-perturbative determination of anisotropy coefficients and pressure gap at the deconfining transition of QCD

We propose a new non-perturbative method to compute derivatives of gauge
coupling constants with respect to anisotropic lattice spacings (anisotropy
coefficients). Our method is based on a precise measurement of the finite
temperature deconfining transition curve in the lattice coupling parameter
space extended to anisotropic lattices by applying the spectral density method.
We determine the anisotropy coefficients for the cases of SU(2) and SU(3) gauge
theories. A longstanding problem, when one uses the perturbative anisotropy
coefficients, is a non-vanishing pressure gap at the deconfining transition
point in the SU(3) gauge theory. Using our non-perturbative anisotropy
coefficients, we find that this problem is completely resolved.Comment: LATTICE98(hightemp

### On the Continuum Limit of the Discrete Regge Model in 4d

The Regge Calculus approximates a continuous manifold by a simplicial
lattice, keeping the connectivities of the underlying lattice fixed and taking
the edge lengths as degrees of freedom. The Discrete Regge model employed in
this work limits the choice of the link lengths to a finite number. This makes
the computational evaluation of the path integral much faster. A main concern
in lattice field theories is the existence of a continuum limit which requires
the existence of a continuous phase transition. The recently conjectured
second-order transition of the four-dimensional Regge skeleton at negative
gravity coupling could be such a candidate. We examine this regime with Monte
Carlo simulations and critically discuss its behavior.Comment: Lattice2002(gravity

### Detailed Phase Transition Study at M_H <= 70 GeV in a 3-dimensional $SU(2)$--Higgs Model

We study the electroweak phase transition in an effective 3-dimensional
theory for a Higgs mass of about 70 GeV by Monte Carlo simulations. The
transition temperature and jumps of order parameters are obtained and
extrapolated to the continuum using multi-histogram techniques and finite size
analysis.Comment: Talk presented at LATTICE96(electroweak), 4 pages, 5 figure

### Atomization and mixing study

The state of the art in atomization and mixing for triplet, pentad, and coaxial injectors is described. Injectors that are applicable for LOX/hydrocarbon propellants and main chamber and fuel rich preburner/gas generator mixture ratios are of special interest. Various applicable correlating equations and parameters as well as test data found in the literature are presented. The validity, utility, and important aspects of these data and correlations are discussed and the measurement techniques used are evaluated. Propellant mixing tests performed are described and summarized, results are reported, and tentative conclusions are included

### Strong Coupling Lattice Schwinger Model on Large Spherelike Lattices

The lattice regularized Schwinger model for one fermion flavor and in the
strong coupling limit is studied through its equivalent representation as a
restricted 8-vertex model. The Monte Carlo simulation on lattices with
torus-topology is handicapped by a severe non-ergodicity of the updating
algorithm; introducing lattices with spherelike topology avoids this problem.
We present a large scale study leading to the identification of a critical
point with critical exponent $\nu=1$, in the universality class of the Ising
model or, equivalently, the lattice model of free fermions.Comment: 16 pages + 7 figures, gzipped POSTSCRIPT fil

### Compact U(1) Gauge Theory on Lattices with Trivial Homotopy Group

We study the pure gauge model on a lattice manifold with trivial fundamental
homotopy group, homotopically equivalent to an $S_4$. Monopole loops may
fluctuate freely on that lattice without restrictions due to the boundary
conditions. For the original Wilson action on the hypertorus there is an
established two-state signal in energy distribution functions which disappears
for the new geometry. Our finite size scaling analysis suggests stringent upper
bounds on possible discontinuities in the plaquette action. However, no
consistent asymptotic finite size scaling behaviour is observed.Comment: 18 pages (3 figures), LaTeX + POSTSCRIPT (287 KB), preprint BI-TP
94/3

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