Mean-field Exponents Research Articles

A new phase for the anisotropic N=4 super Yang-Mills plasma

Black hole solutions of type IIB supergravity have been previously constructed that describe the N=4 supersymmetric Yang-Mills plasma with an anisotropic spatial deformation. The zero temperature limit of these black holes approach a Lifshitz-like scaling solution in the infrared. We show that these black holes become unstable at low temperature and we construct a new class of black hole solutions which are thermodynamically preferred. The phase transition is third order and incorporates a spontaneous breaking of the $SO(6)$ global symmetry down to $SO(4)\times SO(2)$. The critical exponents for the phase transition are given by $(\alpha,\beta,\gamma,\delta)=(-1,1,1,2)$ which differ from the standard mean-field exponents usually seen in holography. At low temperatures the black holes approach a novel kind of scaling behaviour in the far IR with spatial anisotropy and hyperscaling violation. We show that the new ground states are thermal insulators in the direction of the anisotropy.

Critical behavior in spherical and hyperbolic spaces

We study the effects of curved background geometries on the critical behavior of scalar field theory. In particular we concentrate on two maximally symmetric spaces: d-dimensional spheres and hyperboloids. In the first part of the paper, by applying the Ginzburg criterion, we find that for a large correlation length the Gaussian approximation is valid on the hyperboloid for any dimension d ⩾ 2, while it is not trustable on the sphere for any dimension. This is understood in terms of various notions of the effective dimension, such as the spectral and Hausdorff dimension. In the second part of the paper, we apply functional renormalization group methods to develop a different perspective on such phenomena and to deduce them from a renormalization group analysis. By making use of the local potential approximation, we discuss the consequences of having a fixed scale in the renormalization group equations. In particular, we show that in the case of spheres there is no true phase transition, as symmetry restoration always occurs at large scales. In the case of hyperboloids, the phase transition is still present, but as the only true fixed point is the Gaussian one, mean field exponents are valid also in dimensions lower than four.

Critical scaling analysis of the itinerant ferromagnetSr1−xCaxRuO3

The critical behavior of ${\mathrm{Sr}}_{1\ensuremath{-}x}$${\mathrm{Ca}}_{x}$${\mathrm{RuO}}_{3}$ was investigated by a scaling analysis based on the Arrott-Noakes equation of state. The critical exponents \ensuremath{\beta}, \ensuremath{\gamma}, and \ensuremath{\delta} of the magnetic critical behavior were extracted for samples with 0 $\ensuremath{\le}x\ensuremath{\le}0.6$ . The ferromagnetic system exhibits a smooth suppression of the Curie temperature ${T}_{\mathrm{C}}$ to zero at a critical concentration ${x}_{c}$ \ensuremath{\approx} 0.7. The ordered magnetic moment decreases simultaneously as expected for itinerant ferromagnets, however, does not vanish completely at ${x}_{\mathrm{c}}$, indicating small magnetic clusters or inhomogeneities. For $x$ = 0, mean-field like exponents are observed. With increasing $x$, the critical exponents \ensuremath{\beta}, \ensuremath{\gamma}, and \ensuremath{\delta} vary nearly linearly from \ensuremath{\beta} \ensuremath{\approx} 0.5, \ensuremath{\gamma} \ensuremath{\approx} 1, and \ensuremath{\delta} \ensuremath{\approx} 3 for $x$ = 0 to \ensuremath{\beta} \ensuremath{\approx} 1, \ensuremath{\gamma} \ensuremath{\approx} 0.9, and \ensuremath{\delta} \ensuremath{\approx} 1.6 for $x$ \ensuremath{\approx} 0.6. The Widom scaling relation is always met for $x\ensuremath{\le}0.6.$ Despite the systematic evolution of the critical exponents as a function of $x$, the exponents cannot be described by any of the universality classes known for classical standard models. The particular trend of the effective critical exponents may be possibly explained by a strong-disorder line of fixed points; the vicinity to ${x}_{c}$ suggests that this behavior is caused by the vicinity to a quantum phase transition.

Design, Synthesis and Analysis of Chlorohydroquinone Derivatives—Liquid Crystalline Complexes

A novel linear double hydrogen-bonded liquid crystalline material is designed and isolated. The ingredients of the mesogens synthesized are chloro hydroquinone (ClHQ) and p-n alkyloxy benzoic acid (nBAO) where n varied from pentyl to dodecyl alkyloxy carbon numbers. The series is abbreviated as ClHQ + nBAO, and seven of eight synthesized complexes are found to exhibit liquid crystalline phases. These liquid crystalline complexes are characterized by Fourier Transformation Infrared spectroscopy (FTIR) in order to confirm the formation of hydrogen bond. Mesophases and their corresponding transition temperatures are studied by polarizing optical microscopy (POM) and their respective enthalpy values along with the order of the transitions are determined by Differential Scanning Calorimetry (DSC). The experimental measurement of tilt angle is carried out by optical extinction method and fitted to the theoretically predicted mean field exponent which is found to be in good agreement. Dielectric relaxations at different temperatures in nematic phase for the complexes have been carried out and their corresponding activation energy values are calculated from Cole–Davidson plots. Light filtering action in the liquid crystalline complexes is done to validate the commercial applications of these mesogens.

Enhancement of chiral symmetry breaking from the pion condensation at finite isospin chemical potential in a holographic QCD model

We study the pion condensation at finite isospin chemical potential using a holographic QCD model. By solving the equations of motion for the pion fields together with those for the iso-singlet scalar and iso-triplet vector meson fields, we show that the phase transition from the normal phase to the pion condensation phase is second order with the mean field exponent, and that the critical value of the isospin chemical potential $\mu_I$ is equal to the pion mass, consistently with the result obtained by the chiral effective Lagrangian at $O(p^2)$. For higher chemical potential, we find a deviation, which can be understood as a higher order effect in the chiral effective Lagrangian. We investigate the $\mu_I$-dependence of the chiral condensate defined by $\tilde{\sigma} \equiv \sqrt{ \langle \sigma \rangle^2 + \langle \pi^a \rangle^2 }$. We find that $\tilde{\sigma}$ is almost constant in the small $\mu_I$ region, while it grows with $\mu_I$ in the large $\mu_I$ region. This implies that the strength of the chiral symmetry breaking is not changed for small $\mu_I$: The isospin chemical potential plays a role to rotate the "vacuum angle" of the chiral circle $\tan^{-1} \sqrt{ \langle \pi^a \rangle^2 / \langle \sigma \rangle^2 } $ with keeping the "radius" $\tilde{\sigma}$ unchanged for small $\mu_I$. For large $\mu_I$ region, on the other hand, the chiral symmetry breaking is enhanced by the existence of $\mu_I$.

Intertwining of Frustration with Magneto-Elastic Coupling in the Multiferroic LuMnO3

Residual magnetic frustration in the multiferroic LuMnO3 may be key towards understanding magneto-elastic coupling in hexagonal manganites. Critical magnetic scattering present well above the magnetic ordering temperature TN persists below, as observed by inelastic neutron scattering. The magnetic fluctuations are confined in two dimensions implied by the characteristic wavevector dependence of the magnetic structure factor that changes from symmetric to asymmetric across TN. The low dimensionality of the magnetic structure is also evident in the temperature dependence of the commensurate antiferromagnetic intensity which follows a mean field exponent of β ∼ 0.2.

Nature of synchronization transitions in random networks of coupled oscillators

We consider a system of phase oscillators with random intrinsic frequencies coupled through sparse random networks and investigate how the connectivity disorder affects the nature of collective synchronization transitions. Various distribution types of intrinsic frequencies are considered: uniform, unimodal, and bimodal distribution. We employ a heterogeneous mean-field approximation based on the annealed networks and also perform numerical simulations on the quenched Erdös-Rényi networks. We find that the connectivity disorder drastically changes the nature of the synchronization transitions. In particular, the quenched randomness completely wipes away the diversity of the transition nature, and only a continuous transition appears with the same mean-field exponent for all types of frequency distributions. The physical origin of this unexpected result is discussed.

Phase diagram structure of topological Mott transition for zero-gap semiconductors beyond conventional Landau-Ginzburg-Wilson scenario

We show that a wide class of unconventional quantum criticality emerges when orbital currents cause quantum phase transitions from zero-gap semiconductors such as Dirac fermions to topological insulator (TI) or Chern insulator (CI). Changes in Fermi surface topology concomitant with (SU(2) or time reversal) symmetry breakings generate quantum critical lines (QCL) even beyond the quantum critical point. This QCL running at temperature $T=0$ separates two distinct topological phases. This is in contrast to the simple termination of the finite temperature critical line at the quantum critical point without any extension of it at $T=0$. Topology change causes the unconventionality beyond the concept of simple spontaneous symmetry breaking assumed in the conventional Landau-Ginzburg-Wilson (LGW) scenario. The unconventional universality implied by mean-field critical exponents beta>1/2 and delta<3 is protected by the existence of the quantum critical line. It emerges for several specific lattice models including the honeycomb, kagome, diamond and pyrochlore lattices. We also clarify phase diagrams of the topological phases in these lattices at finite temperatures.

Mott Metal-Insulator Transition on Compressible Lattices

The critical properties of the finite temperature Mott end point are drastically altered by a coupling to crystal elasticity, i.e., whenever it is amenable to pressure tuning. Similar as for critical piezoelectric ferroelectrics, the Ising criticality of the electronic system is preempted by an isostructural instability, and long-range shear forces suppress microscopic fluctuations. As a result, the end point is governed by Landau criticality. Its hallmark is, thus, a breakdown of Hooke's law of elasticity with a nonlinear strain-stress relation characterized by a mean-field exponent. Based on a quantitative estimate, we predict critical elasticity to dominate the temperature range ΔT*/T(c)≃8%, close to the Mott end point of κ-(BEDT-TTF)(2)X.

Holographic description of finite-size effects in strongly coupled superconductors

Despite its fundamental and practical interest, the understanding of mesoscopic effects in strongly coupled superconductors is still limited. Here we address this problem by studying holographic superconductivity in a disk and a strip of typical size $\ensuremath{\ell}$. For $\ensuremath{\ell}&lt;{\ensuremath{\ell}}_{c}$, where ${\ensuremath{\ell}}_{c}$ depends on the chemical potential and temperature, we have found that the order parameter vanishes. The superconductor-metal transition at $\ensuremath{\ell}={\ensuremath{\ell}}_{c}$ is controlled by mean-field critical exponents, which suggests that quantum and thermal fluctuations induced by finite-size effects are suppressed in holographic superconductors. Intriguingly, the effective interactions that bind the order parameter increase as $\ensuremath{\ell}$ decreases. Most of these results are consistent with experimental observations in Pb nanograins at low temperature and are qualitatively different from the ones expected in a weakly coupled superconductor.

Black branes in a box: hydrodynamics, stability, and criticality

We study the effective hydrodynamics of neutral black branes enclosed in a finite cylindrical cavity with Dirichlet boundary conditions. We focus on how the Gregory-Laflamme instability changes as we vary the cavity radius R. Fixing the metric at the cavity wall increases the rigidity of the black brane by hindering gradients of the redshift on the wall. In the effective fluid, this is reflected in the growth of the squared speed of sound. As a consequence, when the cavity is smaller than a critical radius the black brane becomes dynamically stable. The correlation with the change in thermodynamic stability is transparent in our approach. We compute the bulk and shear viscosities of the black brane and find that they do not run with R. We find mean-field theory critical exponents near the critical point.

NOTE ON ANALYTICAL STUDIES OF ONE-DIMENSIONAL HOLOGRAPHIC SUPERCONDUCTORS

We employ the variational method for the Sturm–Liouville eigenvalue problem to analytically study phase transition of one-dimensional holographic superconductors. It is shown that this method is not a very powerful method to analytically calculate the properties of holographic superconductors. From the analytical treatment of scalar operator condensate at critical temperature, we also show that the mean-field critical exponent 1/2 results from the coupling term between scalar field and vector field, which may be an universal property of holographic superconductors with a similar coupling term in their equations of motion.

Non-amenable Cayley graphs of high girth have $p_c &lt; p_u$ and mean-field exponents

In this note we show that percolation on non-amenable Cayley graphs of high girth has a phase of non-uniqueness, i.e., $p_c< p_u$. Furthermore, we show that percolation and self-avoiding walk on such graphs have mean-field critical exponents. In particular, the self-avoiding walk has positive speed.

Quantum tricriticality in transverse Ising-like systems

The quantum tricriticality of d-dimensional transverse Ising-like systems is studied by means of a perturbative renormalization group approach focusing on static susceptibility. This allows us to obtain the phase diagram for 3<d<4, with a clear location of the critical lines ending in the conventional quantum critical points and in the quantum tricritical one, and of the tricritical line for temperature T \geq 0. We determine also the critical and the tricritical shift exponents close to the corresponding ground state instabilities. Remarkably, we find a tricritical shift exponent identical to that found in the conventional quantum criticality and, by approaching the quantum tricritical point increasing the non-thermal control parameter r, a crossover of the quantum critical shift exponents from the conventional value \phi = 1/(d-1) to the new one \phi = 1/2(d-1). Besides, the projection in the (r,T)-plane of the phase boundary ending in the quantum tricritical point and crossovers in the quantum tricritical region appear quite similar to those found close to an usual quantum critical point. Another feature of experimental interest is that the amplitude of the Wilsonian classical critical region around this peculiar critical line is sensibly smaller than that expected in the quantum critical scenario. This suggests that the quantum tricriticality is essentially governed by mean-field critical exponents, renormalized by the shift exponent \phi = 1/2(d-1) in the quantum tricritical region.

Generalized Polaron Ansatz for the Ground State of the Sub-Ohmic Spin-Boson Model: An Analytic Theory of the Localization Transition

The sub-Ohmic spin-boson model possesses a quantum phase transition at zero temperature between a localized and a delocalized phase, whose properties have so far only been extracted by numerical approaches. Here we present an extension of the Silbey-Harris variational polaron ansatz which allows us to develop an analytical theory which correctly describes a continuous transition with mean-field exponents for 0<s<0.5. The critical properties, couplings, and observables we obtain show excellent agreement with existing numerical results, and we give an intuitive microscopic description of the changing correlations between the system and bath which suppress the spin coherence and drive the transition.

Wetting on a spherical wall: Influence of liquid-gas interfacial properties

We study the equilibrium of a liquid film on an attractive spherical substrate for an intermolecular interaction model exhibiting both fluid-fluid and fluid-wall long-range forces. We first reexamine the wetting properties of the model in the zero-curvature limit, i.e., for a planar wall, using an effective interfacial Hamiltonian approach in the framework of the well known sharp-kink approximation (SKA). We obtain very good agreement with a mean-field density functional theory (DFT), fully justifying the use of SKA in this limit. We then turn our attention to substrates of finite curvature and appropriately modify the so-called soft-interface approximation (SIA) originally formulated by Napiórkowski and Dietrich [Phys. Rev. B34, 6469 (1986)] for critical wetting on a planar wall. A detailed asymptotic analysis of SIA confirms the SKA functional form for the film growth. However, it turns out that the agreement between SKA and our DFT is only qualitative. We then show that the quantitative discrepancy between the two is due to the overestimation of the liquid-gas surface tension within SKA. On the other hand, by relaxing the assumption of a sharp interface, with, e.g., a simple "smoothing" of the density profile there, markedly improves the predictive capability of the theory, making it quantitative and showing that the liquid-gas surface tension plays a crucial role when describing wetting on a curved substrate. In addition, we show that in contrast to SKA, SIA predicts the expected mean-field critical exponent of the liquid-gas surface tension.

Improved Measures for the Shape of a Disordered Polymer To Test a Mean-Field Theory of Collapse

We have generated off-lattice self-avoiding random walks (SAWs) by both Lal’s pivot algorithm and by discontinuous molecular dynamics (DMD) simulations. We chose several volume measures to analyze and compare the shapes characterizing ensembles of SAWs. These included the Flory volume defined through the end-to-end distance, the volume corresponding to the radius of gyration of the polymer, the volume of a sphere drawn from the center of polymer mass that encloses or embeds all the monomers in the polymer, the corresponding ellipsoid describing the radius of gyration tensor, the volume of the smallest Cartesian box oriented in a fixed “lab” frame which encloses all polymer monomers, and the volume of the smallest box oriented along the principal axes of the radius of gyration tensor that encloses all polymer monomers. The tensor ellipsoid and principal box correlate well with each other but not with the other measures. There is a substantial amount of polymer that is excluded from the radius of gyration sphere or ellipsoid (approximately 42% and 44% respectively on average), which casts doubt on the utility of these measures in quantitatively characterizing the volume spanned by a polymer configuration. The principal box volume led to the most well-defined length distribution for the SAW in terms of the ratio of standard deviation to the mean, while the end-to-end distribution was the most broadly distributed. In the principal box analysis, polymer configurations are highly anisotropic, with stronger cubic to square prism symmetry breaking than square prism to rectangular cuboid. We introduce the acubicity in analogy with the asphericity and find its distribution, along with a generalization of acubicity that better discriminates polymer anisotropy. We analyze the role of the above volume measures in determining the packing fraction which enters into the “random mixing” mean-field theory for the energy of an isolated homopolymer. Here we find from both pivot and DMD simulations that no particular volume measure reproduces the mean-field scaling exponent (of unity) for the energy as a function of the reciprocal polymer volume. Instead, anomalous exponents are observed which are less than that of mean-field theory, ranging from 0.2 to 0.5 depending on the contact cutoff length. An energy function with such an anomalous scaling may be used in a simple phenomenological theory of coil–globule collapse. We find in particular that the Flory volume does not accurately describe the energy in a mean-field theory. Possible reasons for such anomalous exponents are discussed.

Analytical computation of critical exponents in several holographic superconductors

It is very interesting that all holographic superconductors, such as s-wave, p-wave and d-wave holographic superconductors, show the universal mean-field critical exponent 1/2 at the critical temperature, just like Gindzburg-Landau (G-L) theory for second order phase transitions. Now it is believed that the universal critical exponents appear because the dual gravity theory is classic in the large N limit. However, even in the large N limit there is an exception called “non-mean-field theory”: an extension of the s-wave model with a cubic term of the charged scalar field shows a different critical exponent 1. In this paper, we try to use analytical methods to obtain the critical exponents for these models to see how the properties of the gravity action decides the appearance of the mean-field behaviors. It will be seen that just like the G-L theory, it is the fundamental symmetries rather than the detailed parameters of the bulk theory that lead to the universal properties of the holographic superconducting phase transition. The feasibility of the called “non-mean-field theory” is also discussed.

Publisher’s Note: Latent heat of nuclear matter [Phys. Rev. C83, 024308 (2011)

We study the latent heat of the liquid-gas phase transition in symmetric nuclear matter using self-consistent mean-field calculations with a few Skyrme forces. The temperature dependence of the latent heat is rather independent of the mean-field parametrization and can be characterized by a few parameters. At low temperatures, the latent heat tends to the saturation energy. Near the critical point, the latent heat goes to zero with a well-determined mean-field critical exponent. A maximum value of the latent heat in the range l ~ 25-30 MeV is found at intermediate temperatures, which might have experimental relevance. All these features can be explained from very basic principles.

Latent heat of nuclear matter

We study the latent heat of the liquid-gas phase transition in symmetric nuclear matter using self-consistent mean-field calculations with a few Skyrme forces. The temperature dependence of the latent heat is rather independent of the mean-field parametrization and it can be characterized by a few parameters. At low temperatures, the latent heat tends to the saturation energy. Near the critical point, the latent heat goes to zero with a well-determined mean-field critical exponent. A maximum value of the latent heat in the range l similar to 25-30 MeV is found at intermediate temperatures, which might have experimental relevance. All these features can be explained from very basic principles.