QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

Four-dimensional Yang–Mills theory with a three-dimensional fermion membrane

We study the four-dimensional Yang–Mills theory in the presence of a three-dimensional membrane of fermions by lattice Monte Carlo simulations. We analyze the phase structure of this theory at finite temperature. Below the phase transition temperature of the pure Yang–Mills theory, we obtain an unconventional phase with spatially-nonuniform vacuum. In this phase, the expectation value of the Polyakov loop is finite on the membrane, and it exponentially decays to zero outside the membrane.     

Failure of mean field theory at large N

We study strongly coupled lattice QCD with N colors of staggered fermions in 3+1 dimensions. While mean field theory describes the low temperature behavior of this theory at large N, it fails in the scaling region close to the finite temperature second order chiral phase transition. The universal critical region close to the phase transition belongs to the 3D XY universality class even when N becomes large. This is in contrast to Gross-Neveu models where the critical region shrinks as N (the number of flavors) increases and mean field theory is expected to describe the phase transition exactly in the limit of infinite N. Our work demonstrates that infrared fluctuations can be important close to second order phase transitions even when N is strictly infinite.     

Phase transitions for flat anti-de Sitter black holes

We reexamine the thermodynamics of anti-de Sitter (adS) black holes with Ricci flat horizons using the adS soliton as the thermal background. We find that there is a phase transition which is dependent not only on the temperature but also on the black hole area, which is an independent parameter. As in the spherical adS black hole, this phase transition is related via the adS/conformal-field-theory correspondence to a confinement-deconfinement transition in the large- N gauge theory on the conformal boundary at infinity.     

Resonance superfluidity in a quantum degenerate Fermi gas

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium ((40)K), and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5T(F). Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly coupled fermions to the Bose-Einstein condensation of strongly bound composite bosons.     

Correlated insulated phase suggests bond order between band and mott insulators in two dimensions

We investigate the ground state phase diagram of the half-filled repulsive Hubbard model in two dimensions in the presence of a staggered potential Delta, the so-called ionic Hubbard model, using cluster dynamical mean-field theory. We find that for large Coulomb repulsion, U > Delta, the system is a Mott insulator (MI). For weak to intermediate values of Delta, on decreasing U, the Mott gap closes at a critical value Uc1(Delta) beyond which a correlated insulating phase with possible bond order is found. Further, this phase undergoes a first-order transition to a band insulator (BI) at Uc2(Delta) with a finite charge gap at the transition. For large Delta, there is a direct first-order transition from a MI to a BI with a single metallic point at the phase boundary.     

Scaling in four-dimensional quantum gravity

We discuss scaling relations in four-dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called “baby universe surgery” we study the critical region of the theory. The position of the phase transition is given with high accuracy and some critical exponents are measured. Their values prove that the transition is continuous. We discuss the properties of two distinct phases of the theory. For large values of the bare gravitational coupling constant the internal Hausdorff dimension is two (the elongated phase), and the continuum theory is that of so called branched polymers. For small values of the bare gravitational coupling constant the internal Hausdorff dimension seems to be infinite (the crumpled phase). We conjecture that this phase corresponds to a theory of topological gravity. At the transition point the Hausdorff dimension might be finite and larger than two. This transition point is a potential candidate for a non-perturbative theory of quantum gravity.     

在高密度下核物质的色超导性

建立了相变热力学理论和场论的关系. 强调在量子场论中必须引进序参量场， 则相变的讨论就类似于Goldstone bosons 的产生. 如果只讨论一级相变， Goldstone bosons场就足够了; 如果要讨论二级相变， 则必须讨论一系列的场， 这些场构成一个对称群的表示. 另外, 也将这一思想用到色超导中. In this paper we built a relation between the thermodynamical theory of the phase transition and field theory. We emphasized that in the quantum field theory we have to introduce the order parameter fields. Then the discussion of the phase transition is closed to the creation of the Goldstone bosons. If we only discuss the first order transition, the Goldstone bosons fields are sufficient. If we want to discuss the second order transition, we have to discuss a set of fields that constructs a representation of a symmetry group. We also apply this concept to color superconductivity.     

Freezing of random RNA

We study secondary structures of random RNA molecules by means of a renormalized field theory based on an expansion in the sequence disorder. We show that there is a continuous phase transition from a molten phase at higher temperatures to a low-temperature glass phase. The primary freezing occurs above the critical temperature, with local islands of stable folds forming within the molten phase. The size of these islands defines the correlation length of the transition. Our results include critical exponents at the transition and in the glass phase.     

Chiral phase transition from string theory

The low energy dynamics of a certain D-brane configuration in string theory is described at weak t'Hooft coupling by a nonlocal version of the Nambu-Jona-Lasinio model. We study this system at finite temperature and strong t'Hooft coupling, using the string theory dual. We show that for sufficiently low temperatures chiral symmetry is broken, while for temperatures larger then the critical value, it gets restored. We compute the latent heat and observe that the phase transition is of the first order.     

A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Macroscopic description of the ferromagnetic superconductors

We present an improved analysis of the phase transitions in spin-triplet ferromagnetic superconductors within Ginzburg–Landau theory. We put special emphasis on the phase transitions from normal phase to the mixed phase of coexistence of ferromagnetism and unconventional superconductivity. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions the phase transitions from normal phase to the mixed phase of coexistence of ferromagnetism and unconventional superconductivity are possible when compared to other phase transitions. The conditions for the phase transitions and the stability conditions are calculated. On the basis of this model, it is argued that the transition from normal phase to the mixed phase of coexistence is always of first order. It was observed from the theoretical calculations that the transition from the ferromagnetic phase to the coexistence phase can cross over from the first to the second order at the tricritical point.     

Langevin description of Markov master equations II: Noise correlations

We present experimental results of dielectric and birefringence measurements on 3.5% and 8% Li∶KTaO₃ as a function of temperature. These results indicate that the 8% Li∶KTaO₃ sample undergoes a ferroelectric phase transition at 97 K. The 3.5% sample seems to undergo a distortive transition at ～75 K. Raman experiments show that the splitting of the TO₁ mode of the 8% Li sample extrapolates to zero at ～97 K supporting the conclusion that this sample undergoes a phase transition at this temperature. Raman spectra of both samples at temperatures above the phase transition or freezing temperatures exhibit in addition to second order Raman features first order Raman lines. These lines have the properties of fluctuation induced first order Raman scattering. Measurement of the integrated intensity of these lines is used to obtain the temperature dependence of the fluctuation intensity. The results are compared to the Halperin and Varma theory. The data obtained for the 3.5% Li sample partialy fits the theory. However the results for the 8% Li sample do not fit the theory. The misfit is attributed to the overlap of defect zones.     

Landau-Ginzburg treatment of nuclear matter at finite temperature

Based on recent studies of the temperature dependence of the energy and specific heat of liquid nuclear matter, a phase transition is suggested at a temperature ∼ 0.85 MeV. We apply the Landau-Ginzburg theory to this transition and determine the behaviour of the energy and specific heat close to the critical temperature in the condensed phase. Received: 29 July 2000 / Accepted: 20 October 2000     

Dynamical Hierarchy in Transition States of Reactions

We present a partial normalization procedure of Lie canonical perturbation theory to elucidate the phase space geometry of the transition state in the multidimensional phase space for a wide range of energy above the threshold. State selectivity and dynamical correlation along the evolution of reactions will also be discussed. An erratum to this article is available at .     

Behavior of the antiferromagnetic phase transition near the fermion condensation quantum phase transition in YbRh2Si2

Low-temperature specific-heat measurements on YbRh₂Si₂ at the second order antiferromagnetic (AF) phase transition reveal a sharp peak at TN=72 mK. The corresponding critical exponent α turns out to be α=0.38, which differs significantly from that obtained within the framework of the fluctuation theory of second order phase transitions based on the scale invariance, where α?0.1. We show that under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point leading to a violation of the critical universality of the fluctuation theory. This change of the phase transition is generated by the fermion condensation quantum phase transition. Near the tricritical point the Landau theory of second order phase transitions is applicable and gives α?1/2. We demonstrate that this value of α is in good agreement with the specific-heat measurements.     

Manifestation of critical behavior at first-order phase transitions

We present in this Letter further results which are in good agreement with our earlier observations on the critical behavior at a strong first-order phase transition. More elaborate data analysis has been used here. A quantitative measure of the strength of the transition within the context of Landau theory is also given.     

Ground-state fidelity and bipartite entanglement in the Bose-Hubbard model

We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.     

Phase behavior of binary hard-sphere mixtures from perturbation theory

Using a first-order perturbation theory, we have studied the phase diagram of a binary mixture of hard spheres for different values of the size ratio. Recent models for the two-body depletion potential between large spheres are used to take into account the role of the small spheres. The theory predicts a complex phase diagram including a fluid-solid transition at high packing fraction of small spheres, metastability of fluid-fluid demixing, an isostructural solid-solid transition at high packing fraction of the large spheres for sufficiently small values of the size ratio q of the spheres, and the tendency to sticky-sphere behavior in the limit q-->0. The agreement with recent simulation results is quite good. We also show that this phenomenology was already implicit in the pioneering work of Asakura and Oosawa.