Bengt Petersson

Thermodynamics of SU(3) lattice gauge theory

The pressure and the energy density of the SU(3) gauge theory are calculated on lattices with temporal extent N-tau = 4, 6 and 8 and spatial extent N-sigma = 16 and 32. The results are then extrapolated to the continuum limit. In the investigated temperature range up to five times T-c we observe a 15% deviation from the ideal gas limit. We also present new results for the critical temperature on lattices with temporal extent N, = 8 and 12. At the corresponding critical couplings the string tension is calculated on 32(4) lattices to fix the temperature scale. An extrapolation to the continuum limit yields T-c/root sigma = 0.629(3). We furthermore present results on the electric and magnetic condensates as well as the temperature dependence of the spatial string tension, These observables suggest that the temperature dependent running coupling remains large even at T similar or equal to 5T(c). For the spatial string tension we find root sigma(s)/T = 0.566(13)g(2)(T) with g(2)(5T(c)) similar or equal to 1.5.

Flavours of lagrangian Susskind fermions

Abstract It is shown in this paper how to write the Susskind fermionic action explicitly in terms of flavour Dirac fields defined on hypercubes in position space. The remnant continuous global symmetry is identified with a U(1) V ⊗U(1) A group, where the axial symmetry is flavour non-singlet. This construction allows us to identify the equantum numbers of states found in dynamical calculations for SU( N ) gauge theories, and the currents associated with the above global symmetry. It is also used, in the strong-coupling limit, to compute the decay constant of the pseudo-scalar Goldstone boson associated with the spontaneous breakdown of the U(1) A symmetry. We stress that our construction of flavours leads to a quark propagator which is continuous on the edges of the Brillouin zone, unlike the one obtained by assigning different flavours to different parts of this zone.

EQUATION OF STATE FOR THE SU(3) GAUGE-THEORY

By investigating the SU(3) gauge theory thermodynamics on lattices of various sizes we can control finite lattice cutoff effects. We calculate the pressure and energy density on lattices with temporal extent {ital N}{sub {tau}}=4, 6, and 8 and spatial extent {ital N}{sub {sigma}}=16 and 32, and extrapolate to the continuum limit. We find a deviation from ideal gas behavior of (15--20)%, even at temperatures as high as {ital T}{similar_to}3{ital T}{sub {ital c}}. A calculation of the critical temperature for {ital N}{sub {tau}}=8 and 12 and the string tension for {ital N}{sub {tau}}=32 is performed to fix the temperature scale, yielding {ital T}{sub {ital c}}/{radical}{sigma}=0.629(3) in the continuum limit. {copyright} {ital 1995} {ital The} {ital American} {ital Physical} {ital Society}.

SPONTANEOUS CHIRAL SYMMETRY-BREAKING FOR A U(N) GAUGE-THEORY ON A LATTICE

Abstract We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter 〈 ψ ψ〉 for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.

Focusing on the fixed point of 4D simplicial gravity

Our earlier renormalization group analysis of simplicial gravity is extended. A high-statistics study of the volume and coupling constant dependence of the cumulants of the node distribution is carried out. It appears that the phase transition of the theory is of first order, contrary to what is generally believed.

The theory of dynamical random surfaces with extrinsic curvature

We analyse numerically the critical properties of a two-dimensional discretized random surface with extrinsic curvature embedded in a three-dimensional space. The use of the toroidal topology enables us to enforce the non-zero external extension without the necessity of defining a boundary and allows us to measure directly the string tension. We show that a phase transition from the crumpled phase to the smooth phase observed earlier for a spherical topology appears also for a toroidal surface for the same finite value of the coupling constant of the extrinsic curvature term. The phase transition is characterized by the vanishing of the string tension. We discuss the possible non-trivial continuum limit of the theory, when approaching the critical point. Numerically we find a value of the critical exponent ν to be between 0.38 and 0.42. The specific heat, related to the extrinsic curvature term seems not to diverge (or diverge slower than logarithmically) at the critical point.

Symmetric Hadron Pairs at Large Transverse Momenta as a Test of Hard Scattering Models

The inclusive cross section of hadron pairs produced back-to-back with large transverse momenta is examined in the parton model. It is shown quantitatively that this cross section is determined directly by the hard scattering subprocesses, without being influenced by the internal momentum of the constituents, even for transverse momenta of the order of 2–3 GeV/c. The predictions of the phenomenological quark-quark scattering model and of the quantum chromodynamics model for the back-to-back cross section are compared with recent Fermi-lab data. Predictions are made for the corresponding cross section at ISR-energies.

The acceptance probability in the hybrid Monte Carlo method

Abstract We study the acceptance probability in the hybrid Monte Carlo method applied to lattice QCD with dynamical fermions We investigate in detail its dependence upon the step-size and the parameters β, m q and V , and suggest a simple phenomenological formula for this dependence.

A study of the correlation length near a first-order phase transition : the three-dimensional three-state Potts model

Abstract A high statistics study of the 3-d three-state Potts model on lattices of size L 3 , with L ranging from 12 to 48, confirms the first-order nature of the Z(3) symmetry breaking phase transition in this model. We investigate the behaviour of spin-spin correlations in the critical region, comment on various methods to extract the correlation lengths and point out the resulting ambiguities on finite lattices. Our results indicate a finite correlation length at β c . However, a careful analysis of the correlation functions is necessary to disentangle the inverse mass gap from the tunnelling correlation length which we found to diverge as L at β c although the transition is clearly first order.

A numerical study of discrete euclidean polyakov surfaces

Abstract The results of a computer experiment simulating the behaviour of a version of a discrete Polyakov surface are presented. A non-trivial variation of the fractal dimension of the surface with the dimensionality of the embedding space is found. Fluctuations of the gyration radius and of the coordination number are also considered.