14373820
Critical Hysteresis
Hysteresis is observed at second order phase transitions. Universal scaling for-mulae for the areas of hysteresis loops are written down. Critical exponents are defined, and related to other exponents for static and dynamic critical phenomena. These relations are verified with Langevin dynamics in both the critical and tricriti-cal mean-field models. A finite-size scaling relation is tested in the two-dimensional Ising model with heat-bath dynamics.
119431013
A precise determination of T_c in QCD from scaling
Existing lattice data on the QCD phase transition are analyzed in renormalized perturbation theory. In quenched QCD it is found that T_c scales for lattices with only 3 time slices, and that T_c/Lambda_msbar=1.15 \pm 0.05. A preliminary estimate in QCD with two flavours of dynamical quarks shows that this ratio depends on the quark mass. For realistic quark masses we estimate T_c/Lambda_msbar=0.49 \pm 0.02. We also investigate the equation of state in quenched QCD at 1-loop order in renormalised perturbation theory.
122166973
The phase diagram of QCD: methods and logic of the comparison of experiments and theory
Abstract A small review of the phase diagram of QCD is presented. This is followed by a discussion of the conditions under which experimental data on the fluctuations of conserved quantities in heavy-ion collisions can be treated in the grand canonical ensemble. A robust method for detecting the presence of a nearby critical point in experiments is given. There is a short discussion of the need for non-Gaussian error analysis.
121387686
Hybrid Monte Carlo simulations of a two-dimensional gauge theory
Through a study of the dynamics of the two-dimensional U(1) pure gauge theory we find exponential slowing down in barrier penetration problems. We verify that the dynamical critical exponent in HMC can be tuned exactly to 1, and that normal and gauge fixed updates have equal cost.
17443615
Lattice QCD for RHIC
I briefly introduce the methods by which lattice QCD predictions for RHIC are obtained. Next I deal with lattice determinations of strangeness production and event-to-event fluctuations of conserved quantities. I also present a new diagrammatic method for computing derivatives with respect to chemical potentials, and conclude with discussions of some tests of thermal perturbation theory which follow.
123004962
Flavour degrees of freedom and the transition temperature in QCD
We study the finite temperature transition in QCD with four flavours of dynamical quarks. Our simulation is performed on an 8×16 3 lattice for quarks of mass ma=0.01. At the coupling β c =5.15, we find long-lived metastable states, as well as an abrupt change in the entropy density, suggesting a first order phase transition. Using presently available results from corresponding calculations of the hadron masses and the chiral condensate, this gives us a transition temperature T c ≅100 MeV, which is a factor two lower than the transition temperature found in quenched QCD.
120756008
Supercooling in viscous hydrodynamics for QCD phase transition
First order quark hadron phase transition is considered in scaling hydrodynamics including the Csernai-Kapusta model of nucleation of hadronic bubbles leading to supercooling. The effect of viscosity on the entropy production is studied in ideal as well as in viscous hydrodynamics with and without supercooling. It is found that the excess entropy produced due to supercooling depends weakly on viscosity.
122156675
Relativistic Hadron Model with Intrinsic Mass Splittings
A simple mechanism for the $\mathrm{SU}(3)$-symmetry breaking in strong interactions is introduced by using the formalism of the multispinor field equations, which avoids the use of physical quarks but has resemblance to the quark model. The resulting treatment leads to the Gell-Mann-Okubo mass formula for baryons, but not for mesons. It yields approximate values of -19.5\ifmmode^\circ\else\textdegree\fi{} and 33\ifmmode^\circ\else\textdegree\fi{} for the $\ensuremath{\eta}\ensuremath{-}{\ensuremath{\eta}}^{\ensuremath{'}}$ and $\ensuremath{\varphi}\ensuremath{-}\ensuremath{\omega}$ mixing angles, respectively, and also provides a reasonable explanation for the intermultiplet meson mass formula $m_{K}^{}{}_{}{}^{2}\ensuremath{-}m_{\ensuremath{\pi}}^{}{}_{}{}^{2}=m_{{K}^{*}}^{}{}_{}{}^{2}\ensuremath{-}m_{\ensuremath{\rho}}^{}{}_{}{}^{2}$.
119531408
The thermodynamic model for nuclear multifragmentation
Abstract A great many observables seen in intermediate energy heavy ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble (energy and number of particles in the system are kept fixed), canonical ensemble (temperature and number of particles are kept fixed) or grand canonical ensemble (fixed temperature and a variable number of particles but with an assigned average). This paper deals with calculations with canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in intermediate energy heavy ion collision, to study the caloric curves for nuclei and to explore the possibility of negative specific heat because of the finiteness of nuclear systems. The model can also be used for detailed calculations of other observables not connected with phase transitions, such as populations of selected isotopes in a heavy ion collision. The model also serves a pedagogical purpose. For the problems at hand, both the canonical and grand canonical solutions are obtainable with arbitrary accuracy hence we can compare the values of observables obtained from the canonical calculations with those from the grand canonical. Sometimes, very interesting discrepancies are found. To illustrate the predictive power of the model, calculated observables are compared with data from the central collisions of Sn isotopes.
14808043
Dynamical growth of the hadron bubbles during the quark hadron phase transition
The rate of dynamical growth of the hadron bubbles in a supercooled baryon free quark-gluon plasma is evaluated by solving the equations of relativistic fluid dynamics in all regions. For a nonviscous plasma, this dynamical growth rate is found to depend only on the range of correlation $\ensuremath{\xi}$ of order parameter fluctuation, and the radius R of the critical hadron bubble, the two length scales relevant for the description of the critical phenomena. Further, it is shown that the dynamical prefactor acquires an additive component when the medium becomes viscous. Interestingly, under certain reasonable assumptions for the velocity of the sound in the medium around the saddle configuration, the viscous and the nonviscous parts of the prefactor are found to be similiar to the results obtained by Csernai and Kapusta and Ruggeri and Friedman (for the case of zero viscosity), respectively.
119186084
Bimodality and Coulomb effects with a canonical thermodynamic model
Abstract The effect of the Coulomb interaction on the phase diagram of finite nuclei is studied within the Canonical Thermodynamic Model. If Coulomb effects are artificially switched off, this model shows a phenomenology consistent with the liquid–gas phase transition. The inclusion of Coulomb does not significantly affect the phase diagram but it drastically modifies the nature and order parameter of the transition. A clear understanding of the phenomenon can be achieved looking at the distribution of the largest fragment produced in each fragmentation event. Possible connections with experimental observations are outlined.