Order Thermodynamic Phase Transition Research Articles

Evaporation and information puzzle for 2D nonsingular asymptotically flat black holes

We investigate the thermodynamics and the classical and semiclassical dynamics of two-dimensional (2D), asymptotically flat, nonsingular dilatonic black holes. They are characterized by a de Sitter core, allowing for the smearing of the classical singularity, and by the presence of two horizons with a related extremal configuration. For concreteness, we focus on a 2D version of the Hayward black hole. We find a second order thermodynamic phase transition, separating large unstable black holes from stable configurations close to extremality. We first describe the black-hole evaporation process using a quasistatic approximation and we show that it ends in the extremal configuration in an infinite amount of time. We go beyond the quasistatic approximation by numerically integrating the field equations for 2D dilaton gravity coupled to N massless scalar fields, describing the radiation. We find that the inclusion of large backreaction effects (N ≫ 1) allows for an end-point extremal configuration after a finite evaporation time. Finally, we evaluate the entanglement entropy (EE) of the radiation in the quasistatic approximation and construct the relative Page curve. We find that the EE initially grows, reaches a maximum and then goes down towards zero, in agreement with previous results in the literature. Despite the breakdown of the semiclassical approximation prevents the description of the evaporation process near extremality, we have a clear indication that the end point of the evaporation is a regular, extremal state with vanishing EE of the radiation. This suggests that the nonunitary evolution, which commonly characterizes the evaporation of singular black holes, could be traced back to the presence of the singularity.

Critical exponents for higher order phase transitions: Landau theory and RG flow

In this work, we define and calculate critical exponents associated with higher order thermodynamic phase transitions. Such phase transitions can be classified into two classes: with or without a local order parameter. For phase transitions involving a local order parameter, we write down the Landau theory and calculate critical exponents using the saddle point approximation. Further, we investigate fluctuations about the saddle point and demarcate when such fluctuations dominate over saddle point calculations by introducing the generalized Ginzburg criteria. We use Wilsonian renormalization group (RG) to derive scaling forms for observables near criticality and obtain scaling relations between the critical exponents. Afterwards, we find out fixed points of the RG flow using the one-loop beta function and calculate critical exponents about the fixed points for third and fourth order phase transitions.

Phase diagram of a two-site coupled complex SYK model

We study the thermodynamic properties of a two-site coupled complex Sachdev-Ye-Kitaev (SYK) model in the large $N$ limit by solving the saddle-point Schwinger-Dyson (SD) equations. We find that its phase diagram is richer than in the Majorana case. In the grand canonical ensemble, we identify a region of small chemical potential, and weak coupling between the two SYKs, for which two first order thermodynamic phase transitions occur as a function of temperature. First, we observe a transition from a cold wormhole phase to an intermediate phase that may correspond to a charged wormhole. For a higher temperature, there is another first order transition to the black hole phase. As in the Majorana case, the low temperature wormhole phase is gapped and, for sufficiently large coupling between the two complex SYK, or chemical potential, the first order transitions become crossovers. The total charge is good indicator to study the phase diagram of the model: it is zero in the cold wormhole phase and jumps discontinuously at the temperatures at which the transitions take place. Based on the approximate conformal symmetry of the ground state, expected to be close to a thermofield double state, we identify the effective low energy action of the model. It is a generalized Schwarzian action with $SL(2,R)\times U(1)$ symmetry with an additional potential and a extra degree of freedom related to the charge. In the large $N$ limit, results from this low energy action are consistent with those from the solution of the SD equations. Our findings are a preliminary step towards the characterization of traversable wormholes by its field theory dual, a strongly interacting fermionic system with charger, that is easier to model experimentally.

Field-cooled state of the canonical spin glass revisited

Canonical spin-glass (SG) is an enigmatic system in condensed matter physics. In spite of the intense activities of last five decades several questions regarding the nature of the SG phase transition and the SG ground state are yet to be resolved completely. In this backdrop we have revisited the field cooled state of canonical spin-glass. We have experimentally studied magnetic response in two canonical spin-glass systems AuMn(1.8%) and AgMn(1.1%), both in the field cooled (FC) as well as zero field cooled (ZFC) state. We show that the well known magnetic memory effect, which clearly established earlier the metastable nature of the ZFC state in SG, is also present in the FC state. The results of our experimental study indicate that the FC state also is a non-equilibrium state, and hence the energy landscape involved is a non-trivial one. This in turn seriously questions the picture of spin-glass transformation as a second order thermodynamic phase transition.

Heat capacity and nuclear magnetic relaxation times of non-freezing water restrained by polysaccharides, revisited

Calorimetric and nuclear magnetic relaxation studies on non-freezing water restrained by polysaccharide are introduced together with the historical background of this research field. Non-freezing water restrained by the hydrophilic group of polysaccharide shows no first order thermodynamic phase transition. The amount of non-freezing water calculated from the melting enthalpy of water restrained by various kinds of polysaccharides was collected. Molecular motion of polysaccharides is markedly enhanced by the introduction of non-freezing water and glass transition shifts to the ca. 200 K low temperature side. At the same time, molecular chains rearrange to a more stabilized state, which can be observed as the decrease in heat capacities. 1H nuclear magnetic relaxation studies at a temperature lower than glass transition indicate that a part of the water molecules is closely bound to the backbone proton and is not sufficiently isolated. Calorimetric and nuclear magnetic relaxation studies suggest that non-freezing water inevitably cooperates with matrix polysaccharide molecules.

Phase transitions and geometrothermodynamics of regular black holes

In this paper we study the thermodynamics and state space geometry of regular black hole solutions such as Bardeen black hole, Ay\'{o}n-Beato and Garc\'{i}a black hole, Hayward black hole and Berej-Matyjasek-Trynieki-Wornowicz black hole. We find that all these black holes show second order thermodynamic phase transitions(SOTPT) by observing discontinuities in heat capacity-entropy graphs as well as the cusp type double point in free energy-temperature graph. Using the formulation of geometrothermodynamics we again find the singularities in the heat capacity of the black holes by calculating the curvature scalar of the Legendre invariant metric.

Quasinormal Modes of Phantom Scalar Perturbation in Background of Reissner—Nordström Black Hole

We have investigated the quasinormal modes (QNMs) of phantom scalar perturbation in a Reissner-Nordström (RN) background. We find that the dependence of QNMs on the mass of the field for the phantom perturbation is totally different from that of usual massive perturbation. However, we obtain the same critical value of the overtone number for an angular quantum number from which the mass will begin to have a reverse effect on the real part of QNM frequencies and the perturbation-independent relation between the QNMs and the second order thermodynamic phase transition.

Quasinormal modes and second order thermodynamic phase transition for Reissner–Nordström black hole

The relation between the quasinormal modes (QNMs) and the second order thermodynamic phase transition (SOTPT) for the Reissner–Nordström (RN) black hole is studied. It is shown that the quasinormal frequencies of the RN black hole start to get a spiral-like shape in the complex ω plane and both the real and imaginary parts become the oscillatory functions of the charge if the real part of the quasinormal frequencies arrives at its maximum at the second order phase transition point of Davies for given overtone number and angular quantum number. That is to say, we can find out the SOTPT point from the QNMs of the RN black hole. The fact shows that the quasinormal frequencies carry the thermodynamical information of the RN black hole.

Variational description of the nuclear free energy

By means of a variational calculation, we place an upper bound on the finite-temperature free energy for nuclear systems which can be described by pseudospin Hamiltonians. The trial states are irreducible permutation invariant Gibbs states. The best trial state is the one which minimizes the free energy operator. We compare the upper bound with the numerically computed free energy for the Meshkov-Glick-Lipkin Hamiltonian for various values of nucleon number $N$ and nuclear interaction strength $V$. For large $N$ and/or $\ensuremath{\beta}(=\frac{1}{\mathrm{kT}})$ the best trial Gibbs state becomes a good approximation to the actual density operator. Somewhat surprisingly, the variational approach reveals the presence of a second order thermodynamic phase transition much more clearly than the numerical computation does, even though the former is only an approximation to the latter.NUCLEAR STRUCTURE Finite-temperature free energy, pseudospin Hamiltonian, variational description and phase transitions, atomic coherent states.

Thermodynamics of Solutions with Liquid Crystals Solvents. VII. A Mixture of Cholesteryl Chloride and Cholesteryl Myristate

Abstract Gas-liquid chromatography (glc) was used in a theimodynamic investigation of solubility in a 1.743:1.000 (weight: weight) mixture of Cholesteryl chloride and Cholesteryl myristate. This mixture exhibits a β cholesteric phase (increasing pitch with increasing temperature) at low temperatures, a “nematic point” at 42°C, and an α cholesteric phase (decreasing pitch with increasing temperature) up to 62°C, where a transition to the isotropic liquid takes place. Infinite dilution activity coefficients and partial molar enthalpies of solution were obtained for 16 diverse nonmesomorphic solutes in the β and α phases. The results are interpreted in terms of a statistical thermodynamic model2 of solution in anisotropic solvents. Comparison of solubility behavior in the α and β phases suggests a pronounced difference in the molecular packing of the two phases. Evidence is presented that the β→α transition may involve a higher order thermodynamic phase transition at the “nematic point”.