Fluctuations Of Order Parameter Research Articles

Baryon susceptibilities, non-Gaussian moments, and the QCD critical point

We calculate model-independently the impact of the critical point on higher-order baryon susceptibilities ${\ensuremath{\chi}}_{n}$, showing how they depend on fluctuations of the order parameter. We characterize the kurtosis of the order parameter fluctuations and the baryon moments ${\ensuremath{\chi}}_{3},{\ensuremath{\chi}}_{4}$ as functions on the phase diagram. Important features of this analysis are then confirmed by a Gross--Neveu model study with good qualitative agreement with other model studies. We also compare this to lattice and experimental data. Our results support the universality of the characteristic peak in baryon susceptibilities as a signal of the critical point. We discuss leveraging measurements of different ${\ensuremath{\chi}}_{n}$ to extrapolate the location of the critical point.

Kondo destruction in heavy fermion quantum criticality and the photoemission spectrum of YbRh2Si2

Heavy fermion metals provide a prototype setting to study quantum criticality. Experimentally, quantum critical points have been identified and studied in a growing list of heavy fermion compounds. Theoretically, Kondo destruction has provided a means to characterize a class of unconventional quantum critical points that goes beyond the Landau framework of order-parameter fluctuations. Among the prominent evidence for such local quantum criticality have been measurements in YbRh2Si2. A rapid crossover is observed at finite temperatures in the isothermal field dependence of the Hall coefficient and other transport and thermodynamic quantities, which specifies a T*B line in the temperature (T)–magnetic field (B) phase diagram. Here, we discuss what happens when temperature is raised, by analyzing the ratio of the crossover width to the crossover position. With this ratio approaching unity at T≳0.5K, YbRh2Si2 at zero magnetic field belongs to the quantum-critical fluctuation regime, where the single-particle spectral function has significant weight at both the small and large Fermi surfaces. This implies that, in this temperature range, any measurements sensitive to the Fermi surface will also see a significant spectral weight at the large Fermi surface. The angle-resolved photoemission spectroscopy experiments recently reported for YbRh2Si2 at T>1K are consistent with this expectation, and therefore support the association of the T*B line with the physics of Kondo destruction.

Doping dependence of the critical fluctuation regime in the Fe-based superconductorBa1−xKxFe2As2

We investigate the importance of superconducting order parameter fluctuations in the 122 family of Fe-based superconductors, using high-resolution specific heat and thermal expansion data of various Ba$_{1-x}$K$_x$Fe$_2$As$_2$ single crystals covering a large range of the phase diagram from the strongly underdoped to the overdoped regime. By applying scaling relations of the 3d-XY and the 3d-Lowest-Landau-Level (3d-LLL) fluctuation models to data measured in different magnetic fields, we demonstrate that a strong increase of the critical fluctuation regime is responsible for the transition broadening in magnetic fields, which is a direct consequence of a magnetic-field-induced finite size effect due to a reduction of the effective dimensionality by a decreasing magnetic length scale related to the mean vortex separation and the confinement of quasiparticles in low Landau levels. The fluctuations are stronger in the underdoped and overdoped regimes and appear to be weakest at optimal doping.

Critical behavior of the absorbing transition of branching and annihilating bosonic random walkers

In this work, we investigate the critical behavior of a model describing the parity-conserving branching and annihilating process of random walkers. The model is simulated on a one dimensional lattice on which the sites can be occupied by multiple particles with a finite annhilation probability. We determine the threshold of the phase transition between the statistically stationary active state and the absorbing state. From steady-state simulations and a finite-size scaling analysis, we calculate the order-parameter, order-parameter fluctuations, and spacial correlation length critical exponents. Further, we follow the short-time critical relaxation to provide a set of relevant dynamical critical exponents. We check the validity of the hyperscaling relation for both sets of stationary and dynamical critical exponents. These are consistent with the BARW-PC universality class.

Fluctuation Effects in Phase-Frustrated Multiband Superconductors

In this paper, we compute the phase diagrams of an effective model of a three-dimensional multiband superconductor which is phase-frustrated by interband Josephson couplings. Four different computations are performed and compared: (i) standard mean field theory, (ii) cluster mean field theory, (iii) large-scale Monte Carlo computations including phase fluctuations but no gauge field fluctuations, and (iv) large-scale Monte Carlo computations including phase fluctuations and gauge field fluctuations. Here, phase fluctuations refer to fluctuations in the phases of the components of the superconducting order parameter. Our findings may be summarized as follows: (i) The standard mean field theory treatment fails in locating correctly the positions of the phase transitions, as well as the character of the transitions between the different states. (ii) A cluster mean field calculations taking into account order parameter fluctuations in a local environment improves the results considerably. This shows that phase fluctuations in the superconducting order parameter are important in these three-dimensional systems. The origin of the strong phase fluctuations is frustration due to interband Josephson couplings. However, a novel chiral metallic phase found in previous works using large-scale Monte Carlo computations is not obtained either within the single-site mean field theory or the improved cluster mean field theory of order parameter fluctuations. (iii) Including all phase fluctuations, but no gauge field fluctuations, in the effective model in large-scale Monte Carlo computations yields results essentially in agreement with the cluster mean field calculations. (iv) Including all phase fluctuations and gauge field fluctuations in the effective model in large-scale Monte Carlo computations shows that the inclusion of gauge field fluctuations is crucial in bringing about the novel chiral metallic state in three dimensions.

Correlation Of Bulk And Surface Properties In Bi-Sn And Bi- In Liquid Alloys

We have used simple statistical model to report the energetic and its effect on the alloying behavior of Bi-Sn and Bi-In liquid alloys. The energetic of mixing in liquid alloys has been analyzed through the study of bulk and surface properties. In the bulk, we have studied thermodynamic properties, which include Gibb’s free energy of mixing, enthalpy of mixing and entropy of mixing. The surface behavior has been analyzed by computing surface concentration and surface tension of the alloys. For the microscopic structural investigation our study includes concentration-concentration fluctuation in long wavelength limit and Warren-Cowley short range order parameter, they have been discussed in term of the energetic of the bulk as well as that of the surface part. The computed results are in good agreement with experimental data and support a weak phase-separation tendency in molten Bi-Sn system and ordering behavior in Bi-In system. In both system, temperature dependent energy parameter takes important role to explain bulk and surface properties.

Minima of the fluctuations of the order parameter of global seismicity.

It has been recently shown [N. V. Sarlis, Phys. Rev. E 84, 022101 (2011) and N. V. Sarlis and S.-R. G. Christopoulos, Chaos 22, 023123 (2012)] that earthquakes of magnitude M greater or equal to 7 are globally correlated. Such correlations were identified by studying the variance κ1 of natural time which has been proposed as an order parameter for seismicity. Here, we study the fluctuations of this order parameter using the Global Centroid Moment Tensor catalog for a magnitude threshold Mthres = 5.0 and focus on its behavior before major earthquakes. Natural time analysis reveals that distinct minima of the fluctuations of the order parameter of seismicity appear within almost five and a half months on average before all major earthquakes of magnitude larger than 8.4. This phenomenon corroborates the recent finding [N. V. Sarlis et al., Proc. Natl. Acad. Sci. U.S.A. 110, 13734 (2013)] that similar minima of the seismicity order parameter fluctuations had preceded all major shallow earthquakes in Japan. Moreover, on the basis of these minima a statistically significant binary prediction method for earthquakes of magnitude larger than 8.4 with hit rate 100% and false alarm rate 6.67% is suggested.

Critical slowing down of the charge carrier dynamics at the Mott metal-insulator transition.

We report on the dramatic slowing down of the charge carrier dynamics in a quasi-two-dimensional organic conductor, which can be reversibly tuned through the Mott metal-insulator transition (MIT). At the finite-temperature critical end point, we observe a divergent increase of the resistance fluctuations accompanied by a drastic shift of spectral weight to low frequencies, demonstrating the critical slowing down of the order parameter (doublon density) fluctuations. The slow dynamics is accompanied by non-Gaussian fluctuations, indicative of correlated charge carrier dynamics. A possible explanation is a glassy freezing of the electronic system as a precursor of the Mott MIT.

Stationary and dynamic critical behavior of the contact process on the Sierpinski carpet.

We investigate the critical behavior of a stochastic lattice model describing a contact process in the Sierpinski carpet with fractal dimension d=log8/log3. We determine the threshold of the absorbing phase transition related to the transition between a statistically stationary active and the absorbing states. Finite-size scaling analysis is used to calculate the order parameter, order parameter fluctuations, correlation length, and their critical exponents. We report that all static critical exponents interpolate between the line of the regular Euclidean lattices values and are consistent with the hyperscaling relation. However, a short-time dynamics scaling analysis shows that the dynamical critical exponent Z governing the size dependence of the critical relaxation time is found to be larger then the literature values in Euclidean d=1 and d=2, suggesting a slower critical relaxation in scale-free lattices.

Electronic nematic phase transition in the presence of anisotropy

We study the phase diagram of electronic nematic instability in the presence of xy anisotropy. While a second order transition cannot occur in this case, mean-field theory predicts that a first order transition occurs near van Hove filling and its phase boundary forms a wing structure, which we term a Griffiths wing, referring to his original work of He3-He4 mixtures. When crossing the wing, the anisotropy of the electronic system exhibits a discontinuous change, leading to a meta-nematic transition, i.e., the analog to a meta-magnetic transition in a magnetic system. The upper edge of the wing corresponds to a critical end line, which shows a non-monotonic temperature dependence as a function of the external anisotropy and vanishes at a quantum critical end point for a strong anisotropy. The mean-field phase diagram is, however, very sensitive to fluctuations of the nematic order parameter, yielding a topologically different phase diagram. The Griffiths wing is broken into two pieces. A tiny wing appears close to zero anisotropy and the other is realized for a strong anisotropy. Consequently three quantum critical end points are realized. We discuss that these results can be related to various materials including a cold atom system.

Extreme Thouless effect in a minimal model of dynamic social networks.

In common descriptions of phase transitions, first-order transitions are characterized by discontinuous jumps in the order parameter and normal fluctuations, while second-order transitions are associated with no jumps and anomalous fluctuations. Outside this paradigm are systems exhibiting "mixed-order" transitions displaying a mixture of these characteristics. When the jump is maximal and the fluctuations range over the entire range of allowed values, the behavior has been coined an "extreme Thouless effect." Here we report findings of such a phenomenon in the context of dynamic, social networks. Defined by minimal rules of evolution, it describes a population of extreme introverts and extroverts, who prefer to have contacts with, respectively, no one or everyone. From the dynamics, we derive an exact distribution of microstates in the stationary state. With only two control parameters, N(I,E) (the number of each subgroup), we study collective variables of interest, e.g., X, the total number of I-E links, and the degree distributions. Using simulations and mean-field theory, we provide evidence that this system displays an extreme Thouless effect. Specifically, the fraction X/(N(I)N(E)) jumps from 0 to 1 (in the thermodynamic limit) when N(I) crosses N(E), while all values appear with equal probability at N(I)=N(E).

Аналітичний опис критичної поведінки тривимірного одновісного магнетика в зовнішньому полі з виділенням системи відліку

The critical behavior of systems belonging to the universality class of the three-dimensional Ising model has been studied theoretically. A three-dimensional Ising-like system with exponentially decreasing interaction potential and in the presence of a homogeneous external field was considered in the framework of the collective variables method. A specific feature in the calculation of the partition function and the free energy of a uniaxial magnet consists in singling out a reference system. The role of the latter is played by the molecular-field Hamiltonian. A method to describe the critical behavior with the use of a singled out reference system is developed on the basis of a non-Gaussian (quartic) distribution of order-parameter fluctuations (the p4 model).

Griffiths wings associated with electronic nematic transition

A spatial xy anisotropy generated by a uniaxial pressure and strain can control a phase transition. In particular, the xy anisotropy couples directly to electronic nematic order and thus is expected to play a crucial role in a system exhibiting nematicity. Here we study the phase diagram of an electronic nematic phase transition by introducing the xy anisotropy. In a mean-field theory, we find that a first order transition occurs near van Hove filling and its phase boundary forms a wing structure, which we term a Griffiths wing. The anisotropy of the electronic system exhibits a discontinuous change by crossing the wing, leading to a meta-nematic transition, i.e., the analog to a meta-magnetic transition observed in ferromagnetic systems such as UGe2 and UCoAl. However, in contrast to ferromagnetic systems, the upper edge of the wing shows a non-monotonic temperature dependence. The Griffiths wing interpolates between a two-dimensional system and a nearly one-dimensional system by changing the xy anisotropy. We also study the effect of nematic order-parameter fluctuations in a functional renormalization-group scheme. We find that the Griffiths wing is very sensitive to the fluctuations and is easily broken into two pieces, leading to a phase diagram topologically different from the mean-field result. We discuss that the Griffiths wing associated with nematicity can be related to various materials such as high-Tc cuprates, bilayer ruthenates, quasi-one-dimensional metals, and cold atom systems.

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy.

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order–parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

Cooper pairing in non-Fermi liquids

States of matter with a sharp Fermi-surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include: ${\it (i)}$ quantum critical points associated with the onset of order in metals; ${\it (ii)}$ spinon Fermi-surface (U(1) spin-liquid) state of a Mott insulator; ${\it (iii)}$ Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi-liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of a phase transition in a metal, and demonstrate that the attractive interaction mediated by the order parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi-surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between ${\it (i)}$ $U(1)$ and $Z_2$ spin-liquid states; ${\it (ii)}$ Halperin-Lee-Read and Moore-Read states.

Quantum phase transitions in semilocal quantum liquids

We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (i) a ``bifurcating'' critical point, for which the order parameter remains gapped at the critical point, and thus is not driven by soft order parameter fluctuations. Rather it appears to be driven by ``confinement'' which arises when two fixed points annihilate and lose conformality. On the condensed side, there is an infinite tower of condensed states and the nonlinear response of the tower exhibits an infinite spiral structure; (ii) a ``hybridized'' critical point which can be described by a standard Landau-Ginsburg sector of order parameter fluctuations hybridized with a strongly coupled sector; (iii) a ``marginal'' critical point which is obtained by tuning the above two critical points to occur together and whose bosonic fluctuation spectrum coincides with that postulated to underly the ``Marginal Fermi Liquid'' description of the optimally doped cuprates.

Shear Thickening in Concentrated Soft Sphere Colloidal Suspensions: A Shear Induced Phase Transition

A model of shear thickening in dense suspensions of Brownian soft sphere colloidal particles is established. It suggests that shear thickening in soft sphere suspensions can be interpreted as a shear induced phase transition. Based on a Landau model of the coagulation transition of stabilized colloidal particles, taking the coupling between order parameter fluctuations and the local strain-field into account, the model suggests the occurrence of clusters of coagulated particles (subcritical bubbles) by applying a continuous shear perturbation. The critical shear stress of shear thickening in soft sphere suspensions is derived while reversible shear thickening and irreversible shear thickening have the same origin. The comparison of the theory with an experimental investigation of electrically stabilized colloidal suspensions confirms the presented approach.

Rashba coupling and magnetic order in correlated helical liquids

We study strongly correlated helical liquids with and without Rashba coupling using quantum Monte Carlo simulations of the Kane-Mele model with a Hubbard interaction at the edge. Independent of the Rashba coupling, we find that interactions enhance spin correlations and suppress the spectral weight at the Fermi level. For sufficiently strong interactions, a gap can be observed in the single-particle spectral function. However, based on a finite-size scaling analysis and theoretical arguments, we argue that this gap is closed by order parameter fluctuations in the Luttinger liquid phase even at zero temperature, and filled in by thermally induced kinks in the order parameter in the Mott phase at finite temperatures. While the bosonization suggests an umklapp-driven Mott transition only in the presence of Rashba coupling and hence a significant impact of the latter, our numerical results are almost unaffected by Rashba coupling even at low temperatures.

Isometric fluctuation relations for equilibrium states with broken symmetry.

We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to many condensed-matter physics systems. Here, we establish these relations for magnetic systems and nematic liquid crystals in a symmetry-breaking external field, and we illustrate them on the Curie-Weiss and the XY models. Our relations also have implications for spontaneous symmetry breaking, which are discussed.

Transverse thermoelectric transport in a model of many competing order parameters

Coexisting fluctuations towards various ordered states are ubiquitous in strongly correlated electronic systems. In particular, measurements of underdoped cuprate high-temperature superconductors reveal evidence for short range charge order in parallel to large superconducting fluctuations. Here we use a non-linear sigma model to describe a system with N competing orders, and calculate its transverse thermoelectric transport coefficient in the analytically tractable limit of large N . Our results, which determine the contribution of order parameter fluctuations to the Nernst signal, are appropriate for high temperatures in the case of finite N . They are similar to previously obtained results within a model of Gaussian superconducting fluctuations.