Quantum phase transitions in the bosonic single-impurity Anderson model

We consider a quantum impurity model in which a bosonic impurity level is coupled to a non-interacting bosonic bath, with the bosons at the impurity site subject to a local Coulomb repulsion U. Numerical renormalization group calculations for this bosonic single-impurity Anderson model reveal a zero-temperature phase diagram where Mott phases with reduced charge fluctuations are separated from a Bose-Einstein condensed phase by lines of quantum critical points. We discuss possible realizations of this model, such as atomic quantum dots in optical lattices. Furthermore, the bosonic single-impurity Anderson model appears as an effective impurity model in a dynamical mean-field theory of the Bose-Hubbard model.     

Euler Walk on a Cayley Tree

We describe two possible regimes (dynamic phases) of the Euler walk on a Cayley tree: a condensed phase and a low-density phase. In the condensed phase the area of visited sites grows as a compact domain. In the low-density phase the proportion of visited sites decreases rapidly from one generation of the tree to the next. We describe in detail returns of the walker to the root and growth of the domain of visited sites in the condensed phase. We also investigate the critical behaviour of the model on the line separating the two regimes.     

Wetting phase transitions and critical phenomena in condensed matter

Equilibrium wetting phase transitions and critical phenomena are discussed from a phenomenological point of view. The ubiquitous character of the wetting phase transition is illustrated through its occurrence in a variety of condensed matter systems, ranging from classical fluids to superconductors and Bose-Einstein condensates. The intriguing behaviour of the three-phase contact line and its line tension, at wetting, is an example of a fundamental problem in this field on which much progress has been made.     

Monte Carlo investigations of the influence of structural defects on aging effects and the violation of the fluctuation-dissipation theorem for a nonequilibrium critical behavior in the three-dimensional Ising model

The specific features of a nonequilibrium critical behavior in the three-dimensional structurally disordered Ising model have been studied numerically by the Monte Carlo method. An analysis of the two-time dependence of the autocorrelation function and the dynamic susceptibility for systems with spin concentrations p = 0.8 and 0.6 has revealed the aging effects, which are characterized by a slowing down of the relaxation of the system with an increase in the waiting time, and the violation of the fluctuation-dissipation theorem. The values of the universal limit of fluctuation-dissipation ratio for the considered systems have been obtained using the Monte Carlo method. It has been shown that the presence of structural defects in the system leads to an enhancement of the aging effects and to an increase of the values of the limit of fluctuation-dissipation ratio.     

Kertész line in the three-dimensional compact U(1) lattice Higgs model

The three-dimensional lattice Higgs model with compact U(1) gauge symmetry and unit charge is investigated by means of Monte Carlo simulations. The full model with fluctuating Higgs amplitude is simulated, and both energy as well as topological observables are measured. The data show a Higgs and a confined phase separated by a well-defined phase boundary, which is argued to be caused by proliferating vortices. For fixed gauge coupling, the phase boundary consists of a line of first-order phase transitions at small Higgs self-coupling, ending at a critical point. The phase boundary then continues as a Kertész line across which thermodynamic quantities are non-singular. Symmetry arguments are given to support these findings.     

Kertész line and embedded monopoles in QCD

We propose a new class of defects in QCD which can be viewed as embedded monopoles made of quark and gluon fields. These objects are explicitly gauge invariant and they closely resemble the Nambu monopoles in the standard electroweak model. We argue that the "embedded QCD monopoles" are proliferating in the quark-gluon plasma phase while in the low-temperature hadronic phase the spatial proliferation of these objects is suppressed. At realistic quark masses and zero chemical potential the hadronic and quark-gluon phases are generally believed to be connected by a smooth crossover across which all thermodynamic quantities are nonsingular. We argue that these QCD phases are separated by a well-defined boundary-known as the Kertész line in condensed matter systems-associated with the onset of the proliferation of the embedded QCD monopoles in the quark-gluon plasma phase.     

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of four-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models. Received 1 December 1998 and Received in final form 17 February 1999     

Exploring a possible origin of the QCD critical endpoint

We develop a new model of the QCD critical endpoint by matching the deconfinement phase transition line of quark-gluon bags with the similar line at which the bag surface tension coefficient vanishes. Unlike all previous studies of such models the deconfined phase in our approach is defined not by an essential singularity of the isobaric partition function but its simple pole. As an unexpected result we find out that the first-order phase transition which is usually defined by a discontinuity of the first derivative of the bag system pressure results from a discontinuity of the derivative of surface tension coefficient of quark-gluon bags.     

Holographic insulator/superconductor phase transitions with excited states

We construct a family of solutions of the holographic insulator/superconductor phase transitions with the excited states in the AdS soliton background by using both the numerical and analytical methods. The interesting point is that the improved SturmLiouville method can not only analytically investigate the properties of the phase transition with the excited states, but also the distributions of the condensed fields in the vicinity of the critical point. We observe that, regardless of the type of the holographic model, the excited state has a higher critical chemical potential than the corresponding ground state, and the difference of the dimensionless critical chemical potential between the consecutive states is around 2.4, which is different from the finding of the metal/superconductor phase transition in the Ad S black hole background. Furthermore, near the critical point, we find that the phase transition of the systems is of the second order and a linear relationship exists between the charge density and chemical potential for all the excited states in both s-wave and p-wave insulator/superconductor models.     

The crack tip: a nanolab for studying confined liquids

We study the equilibrium properties of a liquid phase condensed at the nanoscale between the surfaces of a sharp crack in fused silica in a moist controlled atmosphere. The extension of the condensed phase along the fracture is measured by in situ atomic force microscopy phase imaging and it is shown to be determined by a critical distance between the opposite crack surfaces, which is an increasing function of humidity. The present technique is very promising for measuring the properties of confined liquids at the nanoscale as well as for modeling the physics and chemistry of slow crack propagation in glasses.     

Finite-temperature behavior of the lattice abelian Higgs model

We study phase transitions in the lattice version of the abelian Higgs model, a model which can exhibit both spontaneous symmetry breaking and confinement. When the Higgs charge is the basic U(1) unit, we find that the Higgs and confinement regions are not separated by a phase transition and form a single homogenous phase which we call the total screening phase. The model does not undergo a symmetry restoring phase transition at finite temperature.If the Higgs charge is some multiple of the basic unit the model follows the conventional wisdom: there are 3 phases (normal, Higgs and confinement) at zero temperature, two of which disappear above some critical point. We apply the lessons learned from the lattice Higgs model to understand the behavior of the weak interactions at high temperature.In a long appendix we give an intuitive physical picture for the Polyakov-Susskind quark liberating phase transition and show that it is related to the Hagedorn spectrum of a confining model. We end with a collection of effective field theory approximations to various lattice theories.     

Observable dependence of fluctuation-dissipation relations and effective temperatures

We study the nonequilibrium fluctuation-dissipation theorem (FDT) in the glass phase of Bouchaud's trap model. We incorporate an arbitrary observable m and obtain its correlation and response functions in closed form. A limiting nonequilibrium FDT plot is approached at long times for most choices of m. In contrast to standard mean field models, however, the shape of the plot depends nontrivially on the observable, and its slope varies continuously even though there is a single scaling of relaxation times with age. Nonequilibrium FDT plots can therefore not be used to define a meaningful effective temperature T(eff) in this model. Consequences for the wider applicability of an FDT-derived T(eff) are discussed.     

Potential energy landscape and long-time dynamics in a simple model glass

We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained by studying small size samples, we describe the dynamics of the systems in multidimensional configurational space by means of a simple model. This considers the configurational space as a connected network of minima where the dynamics proceeds by jumps described by an appropriate master equation. Using this model we are able to reproduce the long-time dynamics and the low temperature regime. We investigate both the equilibrium regime and the off-equilibrium one, finding those typical glassy behaviors usually observed in the experiments such as (i) a stretched exponential relaxation, (ii) a temperature-dependent stretching parameter, (iii) a breakdown of the Stokes-Einstein relation, and (iv) the appearance of a critical temperature below which one observes a deviation from the fluctuation-dissipation relation as a consequence of the lack of equilibrium in the system.     

Mean Field Dilute Ferromagnet: High Temperature and Zero Temperature Behavior

We study the mean field dilute model of a ferromagnet. We find and prove an expression for the free energy density at high temperature, and at temperature zero. We find the critical line of the model, separating the phase with zero magnetization from the phase with symmetry breaking. We also compute exactly the entropy at temperature zero, which is strictly positive. The physical behavior at temperature zero is very interesting and related to infinite dimensional percolation, and suggests possible behaviors at generic low temperatures. Lastly, we provide a complete solution for a (partially) annealed model. Our results hold both for the Poisson and the Bernoulli versions of the model.     

Theory of the vortex matter transformations in high-Tc superconductor YBCO

Flux line lattice in type II superconductors undergoes a transition into a "disordered" phase such as vortex liquid or vortex glass, due to thermal fluctuations and random quenched disorder. We quantitatively describe the competition between the thermal fluctuations and the disorder using the Ginzburg-Landau approach. The following T-H phase diagram of YBCO emerges. There are just two distinct thermodynamical phases, the homogeneous and the crystalline one, separated by a single first order transition line. The line, however, makes a wiggle near the experimentally claimed critical point at 12 T. The "critical point" is reinterpreted as a (noncritical) Kauzmann point in which the latent heat vanishes and the line is parallel to the T axis. The magnetization, the entropy, and the specific heat discontinuities at melting compare well with experiments.     

Relaxation phenomena at criticality

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the thermodynamic control parameters. The non-equilibrium evolution following this change displays some of the features typically observed in glassy materials, such as ageing, and it can be monitored via dynamic susceptibilities and correlation functions of the order parameter, the scaling behaviour of which is characterized by universal exponents, scaling functions, and amplitude ratios. This universality allows one to calculate these quantities in suitable simplified models and field-theoretical methods are a natural and viable approach for this analysis. In addition, if a statistical system is spatially confined, universal Casimir-like forces acting on the confining surfaces emerge and they build up in time when the temperature of the system is tuned to its critical value. We review here some of the theoretical results that have been obtained in recent years for universal quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the Ising model with Glauber dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting in a film is discussed within the Gaussian model.     

Heterogeneous diffusion in a reversible gel

We introduce a microscopically realistic model of a physical gel and use computer simulations to study its static and dynamic properties at thermal equilibrium. The phase diagram comprises a sol phase, a coexistence region ending at a critical point, a gelation line determined by geometric percolation, and an equilibrium gel phase unrelated to phase separation. The global structure of the gel is homogeneous, but the stress is only supported by a fractal network. The gel dynamics is highly heterogeneous and we propose a theoretical model to quantitatively describe dynamic heterogeneity in gels. We elucidate several differences between the dynamics of gels and that of glass formers.     

The two-dimensional ANNNI model in the CVM approximation

The phase diagram of the two-dimensional ANNNI model is investigated by the cluster variation method (CVM). We confirm the stability of the disordered phase down toT=0 and the absence of a Lifshitz point at finite temperature forK<1/2, whereK the ratio of the second to the first neighbor pair interactions. Two different modulation regimes for the correlation functions of the disordered phase are separated by a disorder line along which theq vector of the susceptibility maximum undergoes a lock-in transition. The study in reciprocal space of the stability of the disordered phase allows us to define a critical line in the phase diagram along which theq vector characterizing the instability is incommensurate. Finally, we show the existence of another Lifshitz point forK tending to infinity.     

Higgs type excitations in cold atom systems

Higgs type excitations are the excitations which give mass to particles. The Higgs type excitations has a critical role both in particle physics and condensed matter physics. In particle physics, the suspected Higgs boson has been found by the Large Hadron Collider (LHC) in 2012. In condensed matter physics, the Higgs type excitations relate to order phase of the system. In this review, we present an overview of recent studies on the Higgs type excitations both in non-interacting and interacting cold atom systems. First, in non-interacting cold atom system, by synthesizing artificial non-Abelian gauge potential, we demonstrate that when a non-Abelian gauge potential is reduced to Abelian potential, the Abelian part constructs spin-orbit coupling, and the non-Abelian part emerges Higgs excitations. Secondly, the Higgs excitations which are the reputed Higgs amplitude mode in interacting cold atom system are discussed. We review the theoretical model and the experimental detection of Higgs amplitude mode in two dimensional superfluid. The observation of both Higgs type excitations in real experiments are also discussed.