Low temperature limit of lattice QCD (original) (raw)
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Approach to the thermodynamic limit in lattice QCD at μ≠0
Physical Review D, 2008
The expectation value of the complex phase factor of the fermion determinant is computed to leading order in the p-expansion of the chiral Lagrangian. The computation is valid for µ < mπ/2 and determines the dependence of the sign problem on the volume and on the geometric shape of the volume. In the thermodynamic limit with Li → ∞ at fixed temperature 1/L0, the average phase factor vanishes. In the low temperature limit where Li/L0 is fixed as Li becomes large the average phase factor approaches one. The results for a finite volume compare well with lattice results obtained by Allton et al.. After taking appropriate limits, we reproduce previously derived results for the ǫ-regime and for 1-dimensional QCD. The distribution of the phase itself is also computed.
Nuclear Physics A, 1987
We discuss the behavior of the zero temperature limit of lattice field theories with finite chemical potential. The finite chemical potential lattice formalism is applied to the free fermion theory and the Gross-Neveu model where results can be compared with analytic solutions. Problems occuring in the application of this formalism in numerical simulations of lattice QCD are discussed.
Heavy Quark Potential in Lattice QCD at Finite Temperature
Quark Confinement and the Hadron Spectrum V, 2003
Results of the study of lattice QCD with two flavors of nonperturbatively improved Wilson fermions at finite temperature are presented. The transition temperature for mπ mρ ∼ 0.8 and lattice spacing a ∼ 0.12 fm is determined. A two-exponent ansatz is successfully applied to describe the heavy quark potential in the confinement phase. * Talk given by V. Bornyakov at "
Lattice QCD thermodynamic results with improved staggered fermions
European Physical Journal C Particles and Fields, 2009
We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of N τ =4,6 and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential and present the isentropic equation of state on lines of constant entropy per baryon number.
Finite Temperature Lattice QCD in the Large N Limit
International Journal of Modern Physics A, 1997
Our aim is to give a self-contained review of recent advances in the analytic description of the deconfinement transition and determination of the deconfinement temperature in lattice QCD at large N. We also include some new results, as for instance in the comparison of the analytic results with Monte Carlo simulations. We first review the general set-up of finite temperature lattice gauge theories, using asymmetric lattices, and develop a consistent perturbative expansion in the coupling βs of the spacelike plaquettes. We study in detail the effective models for the Polyakov loop obtained, in the zeroth order approximation in βs, both from the Wilson action (symmetric lattice) and from the heat kernel action (completely asymmetric lattice). The distinctive feature of the heat kernel model is its relation with two-dimensional QCD on a cylinder; the Wilson model, on the other hand, can be exactly reduced to a twisted one-plaquette model via a procedure of the Eguchi–Kawai type. In th...
Lattice QCD spectra at finite temperature: a random matrix approach
Physics Letters B, 1996
We suggest that the lattice Dirac spectra in QCD at finite temperature may be understood using a gaussian unitary ensemble for Wilson fermions, and a chiral gaussian unitary ensemble for Kogut-Susskind fermions. For Kogut-Susskind fermions, the lattice results by the Columbia group are in good agreement with the spectral distribution following from a cubic equation, both for the valence quark distribution and the anomalous symmetry breaking. We explicitly construct a number of Dirac spectra for Wilson fermions at finite temperature, and use the end-point singularities to derive analytically the pertinent critical lines. For the physical current masses, the matrix model shows a transition from a delocalized phase at low temperature, to a localized phase at high temperature. The localization is over the thermal wavelength of the quark modes. For heavier masses, the spectral distribution reflects on localized states with competitive effects between the quark Compton wavelength and the thermal wavelength. Some further suggestions for lattice simulations are made.
The Approach to the Thermodynamic Limit in Lattice QCD at mu neq0
2007
The expectation value of the complex phase factor of the fermion determinant is computed to leading order in the p-expansion of the chiral Lagrangian. The computation is valid for µ < mπ/2 and determines the dependence of the sign problem on the volume and on the geometric shape of the volume. In the thermodynamic limit with Li → ∞ at fixed temperature 1/L0, the average phase factor vanishes. In the low temperature limit where Li/L0 is fixed as Li becomes large the average phase factor approaches one. The results for a finite volume compare well with lattice results obtained by Allton et al.. After taking appropriate limits, we reproduce previously derived results for the ǫ-regime and for 1-dimensional QCD. The distribution of the phase itself is also computed.
Simulations with lattice QCD at finite density
Nuclear Physics B, 1990
A method proposed by Barbour, Davies and Sabeur is used to expand the grand canonical partition function for QCD on a finite lattice in terms of the canonical partition functions for a fixed number of fermions. We show how the lattice action corresponding to the canonical partition function for a given fermion number can be obtained. The method is not unique to QCD and can be applied to other theories with complex action. This expansion of the GCPF is used to study QCD at finite density. The results of preliminary numerical simulations performed on a 44 lattice are described. Evidence is found for the positivity and continuity of the canonical partition functions as a function of the fermion number. The number density shows a clear signal of a transition at a density (in lattice units) of about 0.35 at /3 = 4.9 and small quark mass.
1998
These notes aim to provide a pedagogical introduction to Lattice QCD. The topics covered include the scope of LQCD calculations, lattice discretization of gauge and fermion (naive, Wilson, and staggered) actions, doubling problem, improved gauge and Dirac actions, confinement and strong coupling expansions, phase transitions in the lattice theory, lattice operators, a general discussion of statistical and systematic errors in simulations of LQCD, the analyses of the hadron spectrum, glueball masses, the strong coupling constant, and the quark masses.