Abstract:
We show how the measured particle ratios can be used to provide non-trivial information about the critical temperature of the QCD phase transition. This is obtained by including the effects of highly massive Hagedorn resonances on statistical models, which are used to describe hadronic yields. The inclusion of Hagedorn states creates a dependence of the thermal fits on the Hagedorn temperature, $T_H$, which is assumed to be equal to $T_c$, and leads to an overall improvement of thermal fits. We find that for Au+Au collisions at RHIC at $\sqrt{s_{NN}}=200$ GeV the best square fit measure, $\chi^2$, occurs at $T_c \sim 176$ MeV and produces a chemical freeze-out temperature of 172.6 MeV and a baryon chemical potential of 39.7 MeV.

Abstract:
The QCD critical point can be found in heavy ion collision experiments via the non-monotonic behavior of many fluctuation observables as a function of the collision energy. The event-by-event fluctuations of various particle multiplicities are enhanced in those collisions that freeze out near the critical point. Higher, non-Gaussian, moments of the event-by-event distributions of such observables are particularly sensitive to critical fluctuations, since their magnitude depends on the critical correlation length to a high power. We present quantitative estimates of the contribution of critical fluctuations to the third and fourth moments of the pion and proton, as well as estimates of various measures of pion-proton correlations, all as a function of the same five non-universal parameters. We show how to use nontrivial but parameter independent ratios among these more than a dozen fluctuation observables to discover the critical point. We also construct ratios that, if the critical point is found, can be used to overconstrain the values of the non-universal parameters.

Abstract:
We discuss the status of thermal model descriptions of particle ratios in central nucleus-nucleus collisions at ultra-relativistic energy. An alternative to the ``Cleymans-Redlich'' interpretation of the freeze-out trajectory is given in terms of the total baryon density. Emphasis is placed on the relation between the chemical equilibration parameters and the QCD phase boundary. Furthermore, we trace the essential difference between thermal model analyses of data from collisions between elementary particles and from heavy ion collisions as due to a transition from local strangeness conservation to percolation of strangeness over large volumes, as occurs naturally in a deconfined medium. We also discuss predictions of the thermal model for composite particle production.

Abstract:
The RHIC Beam Energy Scan focuses on the study of the QCD phase diagram --- temperature ($T$) vs. baryon chemical potential ($\mu_B$). The aim is to verify some predictions from QCD: that a cross-over occurs at $\mu_B$ = 0, that there exists a first-order phase transition at large $\mu_B$ and a critical point at an intermediate $\mu_B$. The spectra and ratios of produced particles can be used to extract $T$ and $\mu_B$ in different energies and system sizes. The STAR experiment has collected data for Au+Au collisions at $\sqrt{s_{NN}}=$ 7.7 GeV, 11.5 GeV, and 39 GeV in the year 2010. We present midrapidity $p_{T}$ spectra, rapidity density, average transverse mass, and particle ratios for identified hadrons from the STAR experiment. The centrality and transverse momentum dependence of the particle yields and ratios are compared to existing data at lower and higher beam energies. The chemical and kinetic freeze-out conditions are extracted from the ratios and particle spectra.

Abstract:
Binder liked ratios of baryon number are firstly suggested in relativistic heavy ion collisions. Using 3D-Ising model, the critical behavior of Binder ratios and ratios of high order cumulants of order parameter are fully presented. Binder ratio is shown to be a step function of temperature. The critical point is the intersection of the ratios of different system sizes between two platforms. From low to high temperature through the critical point, the ratios of third order cumulants change their values from negative to positive in a valley shape, and ratios of fourth order cumulants oscillate around zero. The normalized ratios, like the Skewness and Kurtosis, do not diverge with correlation length, in contrary with corresponding cumulants. Applications of these characters in search critical point in relativistic heavy ion collisions are discussed.

Abstract:
The behaviour of the chiral condensate in QCD is investigated by means of a study of the distribution of the zeros of the partition function in the complex quark mass plane. Simulations are performed at fixed temperature on three different spatial volumes at $\beta=5.04$ and at $\beta=4.9$ and $\beta=5.2$ on a $4^4$ lattice. Evidence is found for a chirally related transition at non-zero quark mass in the intermediate coupling region for $\beta < 5.2 $ but superimposed upon a smooth behaviour for the condensate. The critical mass at which this transition is found is only weakly dependent on the spatial volume and decreas with decreasing temperature.

Abstract:
We compute the collisional energy loss for a heavy quark above the critical temperature in Quantum ChromoDynamics (QCD). We work in the semi Quark-Gluon Plasma, which assumes that this region is dominated by the non-trivial holonomy of the thermal Wilson line. Relative to the result to leading order in perturbation theory, at a fixed value of the coupling constant we generically we find that collisional energy loss is suppressed by powers of the Polyakov loop, l < 1. For small values of the loop, this suppression is linear for the scattering off of light quarks, and quadratic for the scattering off of gluons, or for Compton scattering.

Abstract:
The critical temperature for $\alpha$-particle condensation in nuclear matter with Fermi surface imbalance between protons and neutrons is determined. The in-medium four-body Schr\"odinger equation, generalizing the Thouless criterion of the BCS transition, is applied using a Hartree-Fock wave function for the quartet projected onto zero total momentum in matter with different chemical potentials for protons and neutrons.

Abstract:
We study the QCD phase transition based on the statistical treatment with the bag-model picture of hadrons, and derive a phenomenological relation among the low-lying hadron masses, the hadron sizes and the critical temperature of the QCD phase transition. We apply this phenomenological relation to both full QCD and quenched QCD, and compare these results with the corresponding lattice QCD results. Whereas such a statistical approach works well in full QCD, it results in an extremely large estimate of the critical temperature in quenched QCD, which indicates a serious problem in understanding of the QCD phase transition. This large discrepancy traces back to the fact that enough number of glueballs are not yet thermally excited at the critical temperature T_c \simeq 280 MeV in quenched QCD due to the extremely small statistical factor as exp(-m_G/T_c) \simeq 0.00207. This fact itself has a quite general nature independent of the particular choice of the effective model framework. We are thus arrive at a mystery, namely, what is really the trigger of the deconfinement phase transition.

Abstract:
We study $\l\f^4$ theory using an environmentally friendly finite-temperature renormalization group. We derive flow equations, using a fiducial temperature as flow parameter, develop them perturbatively in an expansion free from ultraviolet and infrared divergences, then integrate them numerically from zero to temperatures above the critical temperature. The critical temperature, at which the mass vanishes, is obtained by integrating the flow equations and is determined as a function of the zero-temperature mass and coupling. We calculate the field expectation value and minimum of the effective potential as functions of temperature and derive some universal amplitude ratios which connect the broken and symmetric phases of the theory. The latter are found to be in good agreement with those of the three-dimensional Ising model obtained from high- and low-temperature series expansions.