[Show abstract][Hide abstract] ABSTRACT: We simulate the Gross-Neveu model in 2+1 dimensions at non-zero baryon density (chemical potential μ ≠ 0). It is possible to formulate this model with a real action and therefore to perform standard hybrid Monte Carlo simulations with μ ≠ 0 in the functional measure. We compare the physical observables from these simulations with simulations using the Glasgow method where the value of μ in the functional measure is fixed at a value μupd. We find that the observables are sensitive to the choice of μupd. We consider the implications of our findings for Glasgow method QCD simulations at μ ≠ 0. We demonstrate that the realisation of the Goldstone mechanism in the Gross-Neveu model is fundamentally different from that in QCD. We find that this difference explains why there is an unphysical transition in QCD simulations at μ ≠ 0 associated with the pion mass scale whereas the transition in the Gross-Neveu model occurs at a larger mass scale and is therefore consistent with theoretical predictions. We note classes of theories which are exceptions to the Vafa-Witten theorem which permits the possibility of formation of baryon number violating diquark condensates.
Nuclear Physics B 09/1999; 557(1-2-557):327-351. DOI:10.1016/S0550-3213(99)00404-6 · 3.93 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate a strongly U(1) gauge theory with fermions and scalars on a three dimensional lattice and analyze whether the cintinuum limit might be a renormalizable theory with dynamical mass generation. Most attention is paid to the weak coupling region where a possible new dynamical mass generation mechanism might exist. There we investigate the mass of the composite fermion, the chiral condensate and the scaling of the Lee-Yang zeros. Comment: 3 pages,4 figures,talk presented at Lattice97(Edinburgh)
[Show abstract][Hide abstract] ABSTRACT: We investigate the critical behaviour of a three-dimensional lattice $\chiU\phi_3$ model in the chiral limit. The model consists of a staggered fermion field, a U(1) gauge field (with coupling parameter $\beta$) and a complex scalar field (with hopping parameter $\kappa$). Two different methods are used: 1) fits of the chiral condensate and the mass of the neutral unconfined composite fermion to an equation of state and 2) finite size scaling investigations of the Lee-Yang zeros of the partition function in the complex fermion mass plane. For strong gauge coupling ($\beta < 1$) the critical exponents for the chiral phase transition are determined. We find strong indications that the chiral phase transition is in one universality class in this $\beta$ interval: that of the three-dimensional Gross-Neveu model with two fermions. Thus the continuum limit of the $\chiU\phi_3$ model defines here a nonperturbatively renormalizable gauge theory with dynamical mass generation. At weak gauge coupling and small $\kappa$, we explore a region in which the mass in the neutral fermion channel is large but the chiral condensate on finite lattices very small. If it does not vanish in the infinite volume limit, then a continuum limit with massive unconfined fermion might be possible in this region, too. Comment: 27 pages, 16 figures
Physical Review D 04/1998; 58(7). DOI:10.1103/PhysRevD.58.074507 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss QCD at non-zero quark number and zero temperature. The simulations use the Glasgow algorithm and are carried out at infinite gauge coupling. Our improved complex zero analysis gives a critical point in agreement with that predicted by the strong coupling expansion and monomer dimer simulations, while the early onset of the number density appears to be unphysical.
[Show abstract][Hide abstract] ABSTRACT: We give here the contents pages for the Proceedings of the Lattice '97 conference (15th International Symposium on Lattice Field Theory) that took place in July 1997 in Edinburgh, Scotland. The contents are in html form with clickable links to the papers that exist on the hep-lat archive. We hope that this will make it easier to access the output of the conference in a systematic way. Comments on how useful this is/ how it could be improved should be sent to c.davies@physics.gla.ac.uk.
[Show abstract][Hide abstract] ABSTRACT: A brief summary of the formulation of QCD at finite chemical potental, μ, is presented. The failure of the quenched approximation to the problem is reviewed.Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential ≈ . However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, (eμ/T), does show signals of critical behaviour in the expected region of chemical potential.Results are presented for a simulation at finite density of the Gross-Neveu model on a 163 lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when μ passed through the value .
[Show abstract][Hide abstract] ABSTRACT: A brief summary of the formulation of QCD at finite chemical potental, $\mu$, is presented. The failure of the quenched approximation to the problem is reviewed. Results are presented for dynamical simulations of the theory at strong and intermediate couplings. We find that the problems associated with the quenched theory persist: the onset of non-zero quark number does seem to occur at a chemical potential $\approx { {m_{\pi}} \over 2}$. However analysis of the Lee-Yang zeros of the grand canonical partition function in the complex fugacity plane, ($e^{\mu/T}$), does show signals of critical behaviour in the expected region of chemical potential. Results are presented for a simulation at finite density of the Gross-Neveu model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations of QCD no pathologies were found when $\mu$ passed through the value $m_{\pi}/2}$. Comment: 14 pages, Latex, 18 eps figures, Review for Tsukuba workshop
[Show abstract][Hide abstract] ABSTRACT: We study QCD at non-zero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point \mu_c in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations. We observe, however, two unphysical critical points: the onset for the number density \mu_o, and \mu_s the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point \mu_c, and offers a new intepretation of \mu_o, which confirms its unphysical nature. The perspectives for future lattice QCD calculations of the properties of dense baryonic matter are briefly discussed. Comment: 36 pages, RevTeX, 13 eps figures
Physical Review D 05/1997; 56(11). DOI:10.1103/PhysRevD.56.7063 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a method of simulating lattice QCD at nonzero chemical potential in the chiral limit. By adding a weak four-fermi interaction to the standard staggered fermion SU(3) QCD action, we produce an algorithm in which the limit of massless fermions is well-behaved and physical. Using configurations at zero chemical potential, and an exact fugacity expansion of the fermion determinant, we can simulate QCD at nonzero chemical potential and evade the notorious problem of the complex action. Small lattice simulations give physical results: At strong gauge coupling the critical chemical potential \mu_c agrees with theoretical expectations and at weak gauge coupling \mu_c is nonzero in the low temperature confined phase of QCD and jumps to zero in the high temperature quark-gluon plasma phase. In all these simulations the quarks are exactly massless and there is a Goldstone pion. Comment: contains .tex file of text and three figures as .epsi files
[Show abstract][Hide abstract] ABSTRACT: We compare the chemical potential associated with the onset of non-zero baryon number density on $6^4$ and $8^4$ lattices at $\beta=5.1$ and ma=0.01. We provide evidence for $Z(3)$ tunnelling. We determine a critical chemical potential of $\mu a \simeq 0.1$ which is unexpectedly low. We also determine the dependence of the onset of the observed phase transition on the quark mass. The physically misleading result of the quenched theory is shown to persist despite the inclusion of the complex fermion determinant. Comment: 3 pages, Latex, 5 postscript figures, Talk presented at LATTICE96(finite temperature)
[Show abstract][Hide abstract] ABSTRACT: In this paper we present a detailed study of the phase structure in the {beta}-{ital m} plane for compact lattice QED. We analyze the scaling properties of the distribution of the partition function zeros in the complex fermion mass plane on 4{sup 4}, 6{sup 4}, 8{sup 4}, and 10{sup 4} lattices. The partition function is numerically evaluated by using two independent methods, based, respectively, on a standard HMC (hybrid Monte Carlo) program and on an alternative approach derived from the MFA (microcanonical fermionic average). The finite size scaling behavior gives strong indications for a first-order phase transition at any value of the fermion mass. The reliability of the result follows from the remarkable agreement between the two independent methods.
[Show abstract][Hide abstract] ABSTRACT: A finite size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the 2-D Hubbard model in the complex chemical potential plane. The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential. Our analysis points to a second-order phase transition with critical exponent ${1\over \delta}={1\over 2}\pm {1\over 3}$ which leads to a divergence of the electronic susceptibility. We interprete these results as reflecting singular behaviour of the density of states in the quasiparticle spectrum. Comment: 8 pages, Revtex
[Show abstract][Hide abstract] ABSTRACT: Yang-Lee analysis of the grand canonical partition function for a Hubbard Model at finite doping is presented. Evaluating the zeros of this function in the complex chemical-potential plane, we observe an onset of a phase transition when the zeros approach the positive real half-axis with spatial increase of the simulated system. The peak of electronic susceptibility is located in the vicinity of the relevant zeros.
[Show abstract][Hide abstract] ABSTRACT: In this paper we study the general distribution of the Lee-Yang zeros in the complex mass plane for compact QED. We determine all the zeros of the partition function at strong, intermediate and weak coupling on a 44 lattice. Our results give a new picture for the general behaviour of the Lee-Yang zeros for different phases of the system.
Physics Letters B 01/1995; 341(3-4):355-360. DOI:10.1016/0370-2693(95)80014-O · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The lowest zeros of the lattice partition function for non-compact QED are found in the complex fermion mass plane on $6^4$, $8^4$ and $10^4$ lattices at intermediate values of the coupling. The scaling of the low lying zeros with lattice size is analysed. Comment: 3 pages, uuencoded compressed postscript file, poster contribution to LAT94
[Show abstract][Hide abstract] ABSTRACT: Yang-Lee analysis of the Grand Canonical Partition Function for Hubbard
model at finite doping level is presented. The distributions of the
zeros in the complex chemical-potential plane indicate an onset of a
phase transition, with a sharp peak of electronic susceptibility.
Physica C Superconductivity 12/1994; 235-240:2425-2426. DOI:10.1016/0921-4534(94)92433-3 · 0.94 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We summarise a calculation of the zeros of the grand canonical partition function for QCD in the complex chemical potential plane. Preliminary results on a 634 lattice are presented and compared with data on a 44 lattice at the same temperature.
[Show abstract][Hide abstract] ABSTRACT: We present a comparative study of Lee-Yang zeros in the complex mass plane for Lattice Compact QED obtained by using two different approaches for simulating fermions: a standard Hybrid MonteCarlo Method and a less conventional method based on the determination of an effective fermion action, known as the Microcanonical Fermionic Average. We present results on the scaling behaviour of the Lee-Yang zeros on 64 and 84 lattices. Talk presented by G. Salina
[Show abstract][Hide abstract] ABSTRACT: We present and compare the distributions of the zeros of the partition functions of SU(3) and compact U(1) on the complex fermion mass plane. The gross features of the distributions are the same but the scaling of the two theories appears to be different at fixed temperature. At intermediate couplings and finite temperature there is evidence for a first order phase transition in the SU(3) condensate. No evidence for a real singularity has been observed in the compact U(1) theory.