New critical properties of the Nambu-Jona-Lasinio model with nonzero chemical potential

It is shown for the first time that the massive-fermion state in the Nambu-Jona-Lasinio model with nonzero chemical potential μ is described by two different phases, the transition between which is second-order. It is proved that both first-and second-order phase transitions, depending on the values of the model parameters, restore the chiral symmetry of the model. Two tricritical points exist in the (μ, M) phase diagram (M is the dynamical fermion mass at μ=0). Zh. éksp. Teor. Fiz. 111, 1921–1934 (June 1997)     

A Model with Simultaneous First and Second Order Phase Transitions

We introduce a two dimensional nonlinear XY model with a second order phase transition driven by spin waves, together with a first order phase transition in the bond variables between two “bond ordered phases”, one with local ferromagnetic order and another with local anti-ferromagnetic order. We also prove that at the transition temperature the bond-ordered phases coexist with a disordered phase as predicted by Domany, Schick and Swendsen [1]. This last result generalizes the result of van Enter and Shlosman [2] We argue that these phenomena are quite general and should occur for a large class of potentials. PACS number: 64.60.Cn, 75.10.Hk     

Helicity modulus, quantum fluctuations, and superconducting transition in a Josephson junction, array

The effect of quantum fluctuations on a phase transition in a two-dimensional Josephson junction array is studied in terms of the two-dimensional XY model. A self-consistent harmonic approximation is used to calculate the linear response of the system to a perturbation by a uniform phase gradient (helicity modulus γ) as a function of dimensionless temperature Θ and of a quantum parameter q appearing due to the finite capacitance of each junction. Calculation of this quantity has permitted us to find the dependence of the Kosterlitz-Thouless transition temperature on q, which within a broad range of q variation is in agreement with the results of a quantum Monte Carlo simulation. Fiz. Tverd. Tela (St. Petersburg) 39, 818–822 (May 1997)     

Phase transitions in quark matter and behaviour of physical observables in the vicinity of the critical end point

We study the chiral phase transition at finite T and μ _B within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite temperature and baryonic chemical potential are investigated: the study of physical quantities, such as the baryon number susceptibility near the CEP, will provide complementary information concerning the order of the phase transition. We also analyze the information provided by the study of the critical exponents around the CEP.     

Density of states near an Anderson transition in a four-dimensional space. Renormalizable models

Asymptotically accurate results are obtained for the average Green function and density of states of a disordered system for a renormalizable class of models (as opposed to the lattice model examined previously [I. M. Suslov, Zh. éksp. Teor. Fiz. 106, 560 (1994)]. For N∼1 (where N is the order of perturbation theory), only the parquet terms corresponding to the higher powers of large logarithms are taken into account. For large N, this approximation is inadequate because of the higher rate of increase with respect to N of the coefficients for the lower powers of the logarithms. The latter coefficients are determined from the renormalization condition for the theory expressed in the form of a Callan-Symanzik equation using the Lipatov asymptote as boundary conditions. For calculating the self-energy at finite momentum, a modification of the parquet approximation, is used that allows the calculations to be done in an arbitrary finite logarithmic approximation, including the principal asymptote in N of the expansion coefficients. It is shown that the phase transition point moves in the complex plane, thereby ensuring regularity of the density of states for all energies and avoiding the “false” pole in such a way that the effective interaction remains logarithmically weak. Zh. éksp. Teor. Fiz. 111, 220–249 (January 1997)     

Hadron-quark phase coexistence in a hybrid MIT-Bag model

The phase transition of hadronic to quark matter and the boundaries of the hadron-quark coexistence phase are studied within the two Equation of State (EoS) models. The relativistic effective mean-field approach with constant and density-dependent meson-nucleon couplings is used to describe hadronic matter, and the MIT-Bag model is adopted to describe quark matter. The boundaries of the mixed phase for different Bag constants are obtained solving the Gibbs equations. We notice that the dependence on the Bag parameter of the critical temperatures (at zero chemical potential) can be well reproduced by a fermion ultrarelativistic quark gas model, without contribution from the hadron part. At variance, the critical chemical potentials (at zero temperature) are very sensitive to the EoS of the hadron sector. Hence, the contribution of the hadronic interaction is much more relevant for the determination of the transition to the quark-gluon plasma at finite baryon density and low T . Moreover, in the low-temperature and finite chemical potential region no solutions of the Gibbs conditions are existing for small Bag-constant values, B < (135 MeV)⁴ . Isospin effects in asymmetric matter appear important in the high chemical-potential regions at lower temperatures, of interest for the inner-core properties of neutron stars and for heavy-ion collisions at intermediate energies.     

The phase diagram of hadronic matter

We interpret the phase structure of hadronic matter in terms of the basic dynamical and geometrical features of hadrons. Increasing the density of constituents of finite spatial extension, by increasing the temperature T or the baryochemical potential μ, eventually “fills the box” and eliminates the physical vacuum. We determine the corresponding transition as a function of T and μ through percolation theory. At low baryon density, this means a fusion of overlapping mesonic bags to one large bag, while at high baryon density, hard-core repulsion restricts the spatial mobility of baryons. As a consequence, there are two distinct limiting regimes for hadronic matter. We compare our results to those from effective chiral model studies.     

First-Order Phase Transition in Potts Models with Finite-Range Interactions

We consider the Q-state Potts model on Z ^d , Q≥ 3, d≥ 2, with Kac ferromagnetic interactions and scaling parameter γ. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for γ small enough there is a value of the temperature at which coexist Q+1 Gibbs states. The proof is obtained by a perturbation around mean-field using Pirogov-Sinai theory. The result is valid in particular for d = 2, Q = 3, in contrast with the case of nearest-neighbor interactions for which available results indicate a second order phase transition. Putting both results together provides an example of a system which undergoes a transition from second to first order phase transition by changing only the finite range of the interaction.     

On the properties of small-world network models

We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a “small-world” behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a “small-world” one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite. [0.5cm] Received 29 March 1999 and Received in final form 21 May 1999     

The QCD phase boundary from quark–gluon dynamics

We study one-flavor QCD at finite temperature and chemical potential using the functional renormalization group. We discuss the chiral phase transition in QCD and its order with its underlying mechanism in terms of quarks and gluons and analyze the dependence of the phase-transition temperature on small quark chemical potentials. Our result for the curvature of the phase boundary at small quark chemical potential relies on only a single input parameter, the value of the strong coupling at the Z mass scale.     

Phase diagrams of (d x 2−y 2+id xy) superconductors on a square lattice

A model of strongly coupled electrons on a square lattice with attraction of the electrons to nearest-neighbor and next-nearest neighbor lattice sites is studied. For this model, the phase diagrams containing d _x ²−y ², d _xy, and (d _x ²−y ²+id _xy) states are constructed in the variables temperature versus chemical potential for different ratios of the corresponding potentials. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 356–360 (10 March 1998)     

Load-induced increase in the concentration and chemical potential of oxygen atoms in YBa2Cu3O6+x near the order-disorder phase transition

It is found that YBa₂Cu₃O_6+x samples subjected to a load absorb oxygen. The phenomenon is associated with a load-induced shift in the phase transition point. In addition, this shift increases the chemical potential of the oxygen atoms in the loaded sample and is a reason for the increased compressibility of the material near the phase transition. Fiz. Tverd. Tela (St. Petersburg) 39, 240–242 (February, 1997)     

New phase in the Nambu-Jona-Lasinio model for nonzero values of the chemical potential

It is shown that in the Nambu-Jona-Lasinio model with nonzero chemical potential there exist two different phases with spontaneous breaking of chiral symmetry and the transition between the phases is a second-order phase transition. The particle number density is nonzero in one phase and identically zero in the other phase. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 313–318 (10 September 1996)     

Phase structure of the linear sigma model with the standard symmetry breaking term

The linear sigma model at finite isospin chemical potential μ and temperature T is systematically studied by means of the Cornwal–Jackiw–Tomboulis (CJT) effective potential calculated in the improved Hartree–Fock (HF) approximation, where the Goldstone theorem and the thermodynamic consistency are respected. It results that in the chiral limit, for μ=0 the chiral phase transition is second order as expected from the general universality arguments, and for μ≠0 the phase diagram for the pion condensation in the (T,μ) plane exhibits a tricritical point which is crossover from first-order to second-order phase transitions. In the physical world, where the chiral symmetry is explicitly broken, the pion condensation occurs at μ=m _π , the pion mass in vacuum, and its phase diagram is basically in agreement with those found from the chiral perturbation theory. The chiral symmetry gets restored at high values of T for fixed μ and of μ for fixed T.     

Large momenta fluctuations of charm quarks in the Quark-Gluon Plasma<Superscript>⋆</Superscript>

We show that large fluctuations of D-mesons kinetic-energy (or momentum) distributions might be a signature of a phase transition to the Quark-Gluon Plasma (QGP). In particular, a jump in the variance of the momenta or kinetic energy, as a function of a control parameter (temperature or Fermi energy at finite baryon densities) might be a signature for a first-order phase transition to the QGP. This behavior is completely consistent with the order parameter defined for a system of interacting quarks both at zero temperature (and finite baryon densities) or at finite temperatures which shows a jump in correspondence with a first-order phase transition to the QGP. The J/Ψ displays exactly the same behavior of the order parameter and of the variance of the D-mesons. We discuss implications for relativistic heavy-ion collisions within the framework of a transport model and possible hints for experimental search.     

Nuclear magnetic resonance of 55Mn in the antiferromagnet CsMnBr3 in a variable longitudinal magnetic field

The spectrum and intensities of NMR lines are investigated experimentally and theoretically for excitation by an alternating magnetic field h‖ parallel to a static field H in the quasi-one-dimensional, six-sublattice antiferromagnet CsMnBr₃. According to theory, two new NMR lines, which are not excited by a transverse magnetic field h _⊥, are observed near the phase transition from triangular to collinear structure (H=H _c ) [JETP 86, 197 (1998)]. Zh. éksp. Teor. Fiz. 115, 2228–2241 (June 1999)     

Modeling of a structural phase transition in La2−x SrxCuO4

The structural, vibrational, and elastic properties of La₂CuO₄ are calculated using a model for calculating the energy of the crystal based on interionic potentials with the multiparticle Jahn-Teller contribution included explicitly. The microscopic reasons for the structural instability of the La₂CuO₄ lattice relative to rotations of the oxygen octahedra are investigated. A structural phase transition from the orthorhombic phase (space group D _2h ¹⁸ ) into the tetragonal phase (space group D _4h ¹⁷ ) under hydrostatic compression of an La_2−x Sr_xCuO₄ crystal is modeled. The (P,x) structural phase diagram for La_2−x Sr_xCuO₄ is constructed. Fiz. Tverd. Tela (St. Petersburg) 41, 1096–1102 (June 1999)     

Random-Cluster Representation of the Blume–Capel Model

The so-called diluted-random-cluster model may be viewed as a random-cluster representation of the Blume–Capel model. It has three parameters, a vertex parameter a, an edge parameter p, and a cluster weighting factor q. Stochastic comparisons of measures are developed for the ‘vertex marginal’ when q ∊ [1,2], and the ‘edge marginal’ when q ∊ [1,∞). Taken in conjunction with arguments used earlier for the random-cluster model, these permit a rigorous study of part of the phase diagram of the Blume–Capel model. Mathematics Subject Classification (2000): 82B20, 60K35.     

Phase transitions and dynamic effects in crystals characterized by single-cell potentials with a multi-well excited state

A study has been made of phase transitions and phase states in crystals whose unit cell potentials have a multi-well excited state. New phase states compared to the conventional order-disorder-type phase-transition models have been revealed. A phase diagram has been constructed. The applicability criteria of the mean field approximation employed are analyzed. A region of parameter variation where the system is close to the tricritical point has been found. It is shown that microdomains of the new phase can efficiently transfer to the original phase within this region, and vice versa, by resonant tunneling. This tunneling has a relaxational nature. Interaction of such a relaxor with an oscillator (the soft mode) creates in this system an efficient mechanism of formation of the central peak. Besides, this model includes a possibility of coexistence of the order-disorder-type and displacive behavior. This coexistence manifests itself, in particular, in an induced phase transition associated with interaction of the order-disorder-type soft mode with the displacive mode for oscillations in the same potential wells. This induced phase transition may serve as a microscopic model of the improper ferroelastic phase transition in the Hg₂Cl₂ model system. This transition may produce a long-range incommensurate phase involving formation of the corresponding domain system, which is likewise in agreement with the case of Hg₂Cl₂. The model developed here can be used also in describing phase transitions in oxygen-octahedron perovskites, where the relative low-symmetry minima of the single-cell potentials can be related to the charge-transfer vibronic excitons. Fiz. Tverd. Tela (St. Petersburg) 39, 547–556 (March 1997)     

On the phase transition d→(s±id) in high-T c superconductors

A model with an attractive potential in the s and d channels is studied. It is found that in a definite interval of the ratio of the s and d components of the potential the model undergoes a second-order phase transition from the d to the (s±id) state, with breaking of time-reversal symmetry. The transition temperature and the jump in the specific heat are calculated. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 570–574 (25 October 1996)