Lattice QCD at finite isospin density and/or temperature

We simulate two-flavour lattice QCD with at a finite chemical potential $\mu_I$ for isospin, and finite temperature. At small $\mu_I$, we determine the position of the crossover from hadronic matter to a quark-gluon plasma as a function of $\mu_I$. At larger $\mu_I$ we observe the phase transition from the superfluid pion-condensed phase to a quark-gluon plasma, noting its change from second order to first order as $\mu_I$ is increased. We also simulate two-flavour lattice QCD at zero quark mass, using an action which includes an additional 4-fermion interaction, at temperatures close to the chiral transition on $N_t=8$ lattices.Comment: 3 pages LaTex, 3 postscript figures. Parallel talk at Lattice2003(nonzero

SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential mu and temperature T and the results are compared to the predictions of Effective Lagrangians. Simulations on 16^4 lattices indicate that at zero T the theory experiences a second order phase transition to a diquark condensate state which is well described by mean field theory. Nonzero T and mu are studied on 12^3 times 6 lattices. For low T, increasing mu takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing T at high mu, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase.Comment: Lattice2002(nonzerot), 3 pages, 3 figure

Likelihood Analysis for Mega-Pixel Maps

The derivation of cosmological parameters from astrophysical data sets routinely involves operations counts which scale as O(N^3) where N is the number of data points. Currently planned missions, including MAP and Planck, will generate sky maps with N_d = 10^6 or more pixels. Simple ``brute force'' analysis, applied to such mega-pixel data, would require years of computing even on the fastest computers. We describe an algorithm which allows estimation of the likelihood function in the direct pixel basis. The algorithm uses a conjugate gradient approach to evaluate chi-squared and a geometric approximation to evaluate the determinant. Monte Carlo simulations provide a correction to the determinant, yielding an unbiased estimate of the likelihood surface in an arbitrary region surrounding the likelihood peak. The algorithm requires O(N_d^{3/2}) operations and O(N_d) storage for each likelihood evaluation, and allows for significant parallel computation.Comment: 9 pages LaTeX including 2 PostScript figures. Additional discussion of conjugate gradient chi-squared algorithm. Matches accepted versio

The QCD phase diagram at nonzero baryon, isospin and strangeness chemical potentials: Results from a hadron resonance gas model

We use a hadron resonance gas model to study the QCD phase diagram at nonzero temperature, baryon, isospin and strangeness chemical potentials. We determine the temperature of the transition from the hadronic phase to the quark gluon plasma phase using two different methods. We find that the critical temperatures derived in both methods are in very good agreement. We find that the critical surface has a small curvature. We also find that the critical temperature's dependence on the baryon chemical potential at zero isospin chemical potential is almost identical to its dependence on the isospin chemical potential at vanishing baryon chemical potential. This result, which holds when the chemical potentials are small, supports recent lattice simulation studies. Finally, we find that at a given baryon chemical potential, the critical temperature is lowered as either the isospin or the strangeness chemical potential are increased. Therefore, in order to lower the critical temperature, it might be useful to use different isotopes in heavy ion collision experiments.Comment: 7 pages, 15 figure

Can the Electroweak Interaction Break Itself?

I examine the possibility that the electroweak interaction breaks itself via the condensation of fermions in large representations of the weak SU(2)_L gauge group.Comment: 10 pages, Latex, no figures. Published in Phys. Lett. B340, 236 (1994)

Non-compact QED(3) coupled to a four-fermi interaction

We present preliminary numerical results for the three dimensional non-compact QED with a weak four-fermion term in the lattice action. Approaches based on Schwinger-Dyson studies, arguments based on thermodynamic inequalities and numerical simulations lead to estimates of the critical number of fermion flavors (below which chiral symmetry is broken) ranging from $N_{fc}=1$ to $N_{fc}=4$. The weak four-fermion coupling provides the framework for an improved algorithm, which allows us to simulate the chiral limit of massless fermions and expose delicate effects.Comment: 3 pages, Contribution to Lattice2004(chiral), Fermilab, June 21-26, 200

Lattice QCD at finite isospin density at zero and finite temperature

We simulate lattice QCD with dynamical $u$ and $d$ quarks at finite chemical potential, $\mu_I$, for the third component of isospin ($I_3$), at both zero and at finite temperature. At zero temperature there is some $\mu_I$, $\mu_c$ say, above which $I_3$ and parity are spontaneously broken by a charged pion condensate. This is in qualitative agreement with the prediction of effective (chiral) Lagrangians which also predict $\mu_c=m_\pi$. This transition appears to be second order, with scaling properties consistent with the mean-field predictions of such effective Lagrangian models. We have also studied the restoration of $I_3$ symmetry at high temperature for $\mu_I > \mu_c$. For $\mu_I$ sufficiently large, this finite temperature phase transition appears to be first order. As $\mu_I$ is decreased it becomes second order connecting continuously with the zero temperature transition.Comment: 23 pages, Revtex, 9 figures. Major revision of sections 3 and 4 to include new analyses of critical scaling which we now find to be in the universality class of mean-field theor

The Phase Diagram of Four Flavor SU(2) Lattice Gauge Theory at Nonzero Chemical Potential and Temperature

SU(2) lattice gauge theory with four flavors of quarks is simulated at nonzero chemical potential $\mu$ and temperature $T$ and the results are compared to the predictions of Effective Lagrangians. Simulations on $16^4$ lattices indicate that at zero $T$ the theory experiences a second order phase transition to a diquark condensate state. Several methods of analysis, including equation of state fits suggested by Chiral Perturbation Theory, suggest that mean-field scaling describes this critical point. Nonzero $T$ and $\mu$ are studied on $12^3 \times 6$ lattices. For low $T$, increasing $\mu$ takes the system through a line of second order phase transitions to a diquark condensed phase. Increasing $T$ at high $\mu$, the system passes through a line of first order transitions from the diquark phase to the quark-gluon plasma phase. Metastability is found in the vicinity of the first order line. There is a tricritical point along this line of transitions whose position is consistent with theoretical predictions.Comment: 42 pages revtex, 25 figures postscrip

Lattice Gauge Theory Simulations at Nonzero Chemical Potential in the Chiral Limit

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 file

A large Nc perspective on the QCD phase diagram

The transition between the hadronic phase and the quark gluon plasma phase at nonzero temperature and quark chemical potentials is studied within the large-Nc expansion of QCD.Comment: 5 page