Superconducting Quantum Critical Point

We study the properties of a quantum critical point which develops in a BCS superconductor when pair-breaking suppresses the transition temperature to zero. The pair fluctuations are characterized by a dynamical critical exponent z=2. Except for very low temperatures, anomalous contribution to the conductivity is proportional to the square root of T in three dimensions, but to 1/T in two dimensions. At lowest temperatures, the conductivity correction varies as T to the power 1/4 in three dimensions, and as ln(1/T) in two.Comment: 3 pages, 3 Postscript figures, Late

Bootstraping the QCD Critical Point

It is shown that hadronic matter formed at high temperatures, according to the prescription of the statistical bootstrap principle, develops a critical point at nonzero baryon chemical potential. The location of the critical point in the phase diagram, however, depends on the detailed knowledge of the partition function of the deconfined phase, near the critical line. In a simplified version of the quark-gluon partition function, the resulting location of the critical point is compared with the solutions of other approaches and in particular with the results of lattice QCD. The proximity of our solution to the freeze-out area in heavy-ion experiments is also discussed.Comment: 10 pages, 3 figures in 4 file

Davies Critical Point and Tunneling

From the point of view of tunneling, the physical meaning of the Davies critical point of a second order phase transition in the black hole thermodynamics is clarified. At the critical point, the nonthermal contribution vanishes so that the black hole radiation is entirely thermal. It separates two phases: one with radiation enhanced by the nonthermal contribution, the other suppressed by the nonthermal contribution. We show this in both charged and rotating black holes. The phase transition is also analyzed in the cases in which emissions of charges and angular momenta are incorporated.Comment: 1+21 pages, 6 figures, minor editorial changes, a version to appear in IJMP

Scaling laws at the critical point

There are two independent critical exponents that describe the behavior of systems near their critical point. However, at the critical point only the exponent $\eta$, which describes the decay of the correlation function, is usually discussed. We emphasize that there is a second independent exponent $\eta'$ that describes the decay of the fourth-order correlation function. The exponent $\eta'$ is related to the exponents determining the behavior of thermodynamic functions near criticality via a fluctuation-response equation for the specific heat. We also discuss a scaling law for $\eta'$.Comment: Revised version, 1 added figure, 3 pages, 1 tabl

Relaxing Near the Critical Point

Critical slowing down of the relaxation of the order parameter is relevant both in early the universe and in ultrarelativistic heavy ion collisions. We study the relaxation rate of the order parameter in an O(N) scalar theory near the critical point to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transition.A lowest order perturbative calculation (two loops in the coupling lambda) reveals the breakdown of perturbation theory for long-wavelength fluctuations in the critical region and the emergence of a hierarchy of scales with hard q>T, semisoft T >> q >> lambda T and soft lambda T>>q loop momenta which are widely separated for weak coupling. The non-perturbative resummation in the large N limit reveals the renormalization of the interaction and the crossover to an effective 3D-theory for soft momenta.The effective 3D coupling goes to the Wilson-Fisher 3D fixed point in the soft limit.The relaxation rate of the order parameter for wave vectors lambda T >>k>> k_{us} or near the critical temperature lambda T>>m_T>>k_{us} with the ultra soft scale k_{us} = [(lambda T)/(4pi)] exp[-(4pi/lambda)] is dominated by classical semisoft loop momentum leading to Gamma(k,T) = lambda T/(2 pi N). For wavectors k<< k_{us} the damping rate is dominated by hard loop momenta and given by Gamma(k,T)=4 pi T/[3N ln(T/k)]. Analogously, for homogeneous fluctuations in the ultracritical region m_T<<k_{us} the damping rate is given by Gamma_0(m_T,T)=4 pi T/[3N ln(T/m_T)]. Thus critical slowing down emerges for ultrasoft fluctuations where the rate is lambda-independent. The strong coupling regime and the shortcomings of the quasiparticle interpretation are discussed.Comment: LaTex, 39 pages, 12 .ps figure

Isolated critical point from Lovelock gravity

For any K(=2k+1)th-order Lovelock gravity with fine-tuned Lovelock couplings, we demonstrate the existence of a special isolated critical point characterized by non-standard critical exponents in the phase diagram of hyperbolic vacuum black holes. In the Gibbs free energy this corresponds to a place wherefrom two swallowtails emerge, giving rise to two first-order phase transitions between small and large black holes. We believe that this is a first example of a critical point with non-standard critical exponents obtained in a geometric theory of gravity.Comment: 5 pages, 2 figure