I propose a method, based on a set of Langevin equations, for bringing classical gauge theories to thermal equilibrium while respecting the set of Gauss' constraints exactly. The algorithm is described in detail for the SU(2) gauge theory with or without the Higgs doublet. As an example of application, canonical average of the maximal Lyapunov exponent is computed for the SU(2) Yang-Mills theory.

We measure the diffusion rate of Chern-Simons number in the (1+1)-dimensional Abelian Higgs model interacting with a realistic heat bath for temperatures between 1/13 and 1/3 times the sphaleron energy. It is found that the measured rate is close to that predicted by one-loop calculation at the lower end of the temperature range considered but falls at least an order of magnitude short of one-loop estimate at the upper end of that range. We show numerically that the sphaleron approximation breaks down as soon as the gauge-invariant two-point function yields correlation length close to the sphaleron size.IPS Research Report No. 93-10 * Supported by the Swiss National Science Foundation. 1Anomalous electroweak baryon-number violation may have played an important role in setting the baryon number of the Universe to its present value [1,2]. At temperatures above the gauge-boson mass scale electroweak baryon-number nonconservation is dominated by hopping over the finite-energy barriers separating topologically distinct vacua of the bosonic sector. Determination of the corresponding transition rate is a challenging nonperturbative problem, even in the range of validity of the classical approximation. At the lower temperature end of that range the barrier crossings are likely to occur in the vicinity of the saddle point (known as a sphaleron) of the energy functional. The rate can then be estimated using a field-theoretic extension of transition-state theory (TST) [17,18]. At higher temperatures this analytic tool is no longer available, and direct measurement of the rate in real-time numerical simulations of a lattice gauge-Higgs system is the only remaining possibility.Analytical saddle-point estimates of the rate in the Standard Model are complicated by the fact that the corresponding sphaleron field configuration is not known exactly. At the same time, numerical real-time simulations of that system in its low-temperature regime carry an enormous computational cost and are yet to be performed [1,3]. In this situation lower-dimensional models become a very useful test ground on which activationtheory predictions can be confronted by numerical experiments [4,5,6,7,8,9,10,11,12,13,14,15]. For this reason the (1+1)-dimensional Abelian Higgs model (AHM) studied numerically in this work has attracted much attention recently [9,4,6,11,12].Determination of the transition rate should include its proper averaging over the canonical ensemble in the phase space of a system in question. One way to achieve that would be to generate the canonical ensemble of initial configurations, subject each of these configurations to the Hamitonian evolution, and average the transition rate over the initial states of the system. Such procedure, while being perfectly valid, is very costly computationally. To date, a single or a small number of initial configurations have been used in Hamiltonian simulations of AHM [9,12]. In addition, preparing initial configurations in case of a gauge theory presents a technical difficulty: if a standa...

We investigate the effect of dynamical fermions on the sphaleron transition rate at finite temperature for the Abelian Higgs model in one spatial dimension. The fermion degrees of freedom are included through bosonization. Using a numerical simulation, we find that massless fermions do not change the rate within the measurement accuracy. Surprisingly, the exponential dependence of the sphaleron energy on the Yukawa coupling is not borne out by the transition rate, which shows a very weak dependence on the fermion mass.

We study the Chern-Simons number diffusion rate in the (1+1)-dimensional latticeAbelian Higgs model at temperatures much higher than, as well as comparable to, the sphaleron energy. It is found that in the high-temperature limit the rate is likely to grow as power 2/3 of the temperature. In the intermediate-temperature regime, our numerical simulations show that very weak temperature dependence of the rate, found in previous work, persists at smaller lattice spacings. We discuss possibilities of relating the observed behavior of the rate to static finite-temperature properties of the model.Comment: 9 pages, LATeX + 4 figures included as postscript files, to be encapsulated using epsf. Text + figures uuencoded. Also available as a compressed postscript file by anonymous ftp from maggia.ethz.ch (login ftp, pw ftp; then: cd pub, binary, get ahm.ps.Z). IPS Research Report No. 94-0

Performance of the Intel iPSC/860 parallel processor for Quantum Chromodynamics codes with dynamical fermions is described. After reviewing the hardware and software environments provided by the manufacturer, the data structures appropriate for the QCD code are described. Techniques for maximum performance are briefly discussed. We achieve a speed of 10–15 Mŕlops per node depending upon how many lattice sites are located on each node.