Zero-temperature Critical Point Research Articles

Statistical physics of frictional grains: Some simple applications of the Edwards statistics

Granular matter like sand is composed of a large number of interacting grains and is, thus, expected to be amenable to a statistical physics treatment. Yet, the frictional properties of grains make the statistical physics of granular matter significantly different from the equilibrium statistical physics of atomic or molecular systems. We use three simple models to illustrate some of the key concepts of the statistical physics introduced by Edwards and co-workers more than 30 years ago to describe shaken granular piles: non-interacting frictional grains attached to a wall by a spring, a chain of frictional grains connected by springs, and a simplified mean-field model of a granular packing. We observe that a chain of frictional grains connected by springs exhibits a critical point at an infinite effective temperature (i.e., infinitely strong shaking) at odds with the zero-temperature critical point generically found in one-dimensional systems at thermal equilibrium in the presence of local interactions.

Intermediate phase induced by dilution in a correlated Dirac Fermi system

Substituting magnetic ions with nonmagnetic ions is a new way to study dilution. Using determinant quantum Monte Carlo calculations, we investigate an interacting Dirac fermion model with the on-site Coulomb repulsion being randomly zero on a fraction $x$ of sites. Based on conductivity, density of states and antiferromagnetic structure factor, our results reveal a novel intermediate insulating phase induced by the competition between dilution and repulsion. With increasing doping level of nonmagnetic ions, this nonmagnetic intermediate phase is found to emerge from the zero-temperature quantum critical point separating a metallic and a Mott insulating phase, whose robustness is proven over a wide range of interactions. Under the premise of strongly correlated materials, we suggest that doping nonmagnetic ions can effectively convert the system back to the paramagnetic metallic phase. This result not only agrees with experiments on the effect of dilution on magnetic order but also provides a possible direction for studies focusing on the metal-insulator transition in honeycomb lattice like materials.

Renormalization group study of marginal ferromagnetism.

When studying the collective motion of biological groups, a useful theoretical framework is that of ferromagnetic systems, in which the alignment interactions are a surrogate of the effective imitation among the individuals. In this context, the experimental discovery of scale-free correlations of speed fluctuations in starling flocks poses a challenge to common statistical physics wisdom, as in the ordered phase of standard ferromagnetic models with O(n) symmetry, the modulus of the order parameter has finite correlation length. To make sense of this anomaly, a ferromagnetic theory has been proposed, where the bare confining potential has zero second derivative (i.e., it is marginal) along the modulus of the order parameter. The marginal model exhibits a zero-temperature critical point, where the modulus correlation length diverges, hence allowing us to boost both correlation and collective order by simply reducing the temperature. Here, we derive an effective field theory describing the marginal model close to the T=0 critical point and calculate the renormalization group equationsat one loop within a momentum shell approach. We discover a nontrivial scenario, as the cubic and quartic vertices do not vanish in the infrared limit, while the coupling constants effectively regulating the exponents ν and η have upper critical dimension d_{c}=2, so in three dimensions the critical exponents acquire their free values, ν=1/2 and η=0. This theoretical scenario is verified by a Monte Carlo study of the modulus susceptibility in three dimensions, where the standard finite-size scaling relations have to be adapted to the case of d>d_{c}. The numerical data fully confirm our theoretical results.

Field theory for zero temperature soft anharmonic spin glasses in a field

We introduce a finite dimensional anharmonic soft spin glass in a field and show how it allows the construction a field theory at zero temperature and the corresponding loop expansion. The mean field level of the model coincides with a recently introduced fully connected model, the KHGPS model, and it has a spin glass transition in a field at zero temperature driven by the appearance of pseudogapped non-linear excitations. We analyze the zero temperature limit of the theory and the behavior of the bare masses and couplings on approaching the mean field zero temperature critical point. Focusing on the so called replicon sector of the field theory, we show that the bare mass corresponding to fluctuations in this sector is strictly positive at the transition in a certain region of control parameter space. At the same time the two relevant cubic coupling constants g 1 and g 2 show a non-analytic behavior in their bare values: approaching the critical point at zero temperature, g 1 → ∞ while g 2 ∝ T with a prefactor diverging at the transition. Along the same lines we also develop the field theory to study the density of states of the model in finite dimension. We show that in the mean field limit the density of states converges to the one of the KHGPS model. However the construction allows a treatment of finite dimensional effects in perturbation theory.

Nonequlibrium magnetic features in a mixed spin (2, 5/2) Ising system driven by the external oscillating magnetic field by path probability method

Utilizing the path probability method, we investigated nonequilibrium magnetic features in a mixed spin (2, 5/2) Ising model Hamiltonian composed of bilinear and crystal-field interactions in the presence of an external oscillating magnetic field. We numerically solved the time dependence of average magnetizations to find the phases in the system. We examined the dynamic magnetizations to obtain dynamic phase transition (DPT) temperatures, the nature of the DPTs, and phases in the system. The dynamic phase diagrams (DPDs) were constructed in reduced temperature and the amplitude of oscillating magnetic field plane for various interaction parameters. We observed that the system gives very rich and interesting topological behaviors of DPDs, such as up to two dynamic tricritical points, six critical end points, a double critical end points, a zero-temperature critical point, one inverse critical end point and a quadruple point depending on interaction parameters. The system also exhibits paramagnetic, six distinct ferrimagnetic and three different nonmagnetic phases as well as up to eleven different mixed or hybrid phases. In addition, the system exhibits the reentrant behavior.

Dynamic multicritical phase diagrams of the mixed spin (2, 5/2) Blume-Emery-Griffiths model with repulsive biquadratic coupling

We investigated the dynamic phase transitions (DPTs) in the mixed spin (2, 5/2) Blume-Emery Griffiths model with repulsive biquadratic interaction in the presence of a time-varying magnetic field. We used the path probability method to obtain the set of the dynamic equations. We numerically solved these dynamic equations to characterize the nature of first- and second-order phase transitions and to find the DPT temperatures as well as obtain the phases in the system. We constructed the dynamic phase diagrams (DPDs) in reduced temperature and amplitude of oscillating magnetic field plane. We observed that the DPDs display richer, complex and more topological various type of phase diagrams. In particular, DPDs exhibit the disordered phase, antiquadrupolar or staggered phase, six different ferrimagnetic phases, three different nonmagnetic phases, and numerous mixed phases. DPDs also display two dynamic tricritical points for only smaller values of crystal-field interactions, multiple critical end and double critical end points, one zero-temperature critical point, one inverse critical end point, and a quadruple point depending on interaction parameters. The system always shows the reentrant behaviors for the higher values of magnetic field amplitude, but it does not exhibit the dynamic tricritical behavior for higher values of crystal-field parameter.

Magnetic features and compensation behaviors of a mixed spin (1/2, 1) Ising ferrimagnetic system on a hexagonal lattice

We studied dynamic magnetic properties and compensation behaviors of a mixed spin (1/2, 1) Ising ferrimagnetic system on a hexagonal lattice within the path probability method that contains more than one rate constants and the average dynamic order parameters were coupled. We found the phases in the system by solving the average dynamic magnetizations. We examined the thermal features of dynamic magnetizations to characterize the nature of the dynamic phase transitions (DPTs) and obtained the DPT temperatures. We constructed the dynamics phase diagrams in six different planes, which contain the dynamic tricritical, critical end, double critical end, zero-temperature critical and multicritical special points as well as the paramagnetic (P), non-magnetic (NM), ferromagnetic (I) fundamental phases and P+I, NM+I mixed or hybrid phases depending on system parameters. We also investigated the dynamic compensation behaviors, and the N-, P-, Q-, R- and the S-types compensation behaviors were found.

Towards elucidation of zero-temperature criticality of the Ising model on 2D dynamical triangulations

We study the zero-temperature criticality of the Ising model on two-dimensional dynamical triangulations to contemplate its physics. As it turns out, an inhomogeneous nature of the system yields an interesting phase diagram and the physics at the zero temperature is quite sensitive about how we cool down the system. We show the existence of a continuous parameter that characterizes the way we approach the zero-temperature critical point and it may enter in a critical exponent.

Low-temperature marginal ferromagnetism explains anomalous scale-free correlations in natural flocks

We introduce a new ferromagnetic model capable of reproducing one of the most intriguing properties of collective behaviour in starling flocks, namely the fact that strong collective order of the system coexists with scale-free correlations of the modulus of the microscopic degrees of freedom, that is the birds' speeds. The key idea of the new theory is that the single-particle potential needed to bound the modulus of the microscopic degrees of freedom around a finite value, is marginal, that is has zero curvature. We study the model by using mean-field approximation and Monte Carlo simulations in three dimensions, complemented by finite-size scaling analysis. While at the standard critical temperature, $T_c$, the properties of the marginal model are exactly the same as a normal ferromagnet with continuous symmetry-breaking, our results show that a novel zero-temperature critical point emerges, so that in its deeply ordered phase the marginal model develops divergent susceptibility and correlation length of the modulus of the microscopic degrees of freedom, in complete analogy with experimental data on natural flocks of starlings.

Reconstructing the quantum critical fan of strongly correlated systems using quantum correlations

Albeit occurring at zero temperature, quantum critical phenomena have a huge impact on the finite-temperature phase diagram of strongly correlated systems, giving experimental access to their observation. Indeed, the existence of a gapless, zero-temperature quantum critical point induces the existence of an extended region in parameter space—the quantum critical fan (QCF)—characterized by power-law temperature dependences of all observables. Identifying experimentally the QCF and its crossovers to other regimes (renormalized classical, quantum disordered) remains nonetheless challenging. Focusing on paradigmatic models of quantum phase transitions, here we show that quantum correlations—captured by the quantum variance of the order parameter—exhibit the temperature scaling associated with the QCF over a parameter region much broader than that revealed by ordinary correlations. The link existing between the quantum variance and the dynamical susceptibility paves the way to an experimental reconstruction of the QCF using spectroscopic techniques.

Signature of quantum Griffiths singularity state in a layered quasi-one-dimensional superconductor

Quantum Griffiths singularity was theoretically proposed to interpret the phenomenon of divergent dynamical exponent in quantum phase transitions. It has been discovered experimentally in three-dimensional (3D) magnetic metal systems and two-dimensional (2D) superconductors. But, whether this state exists in lower dimensional systems remains elusive. Here, we report the signature of quantum Griffiths singularity state in quasi-one-dimensional (1D) Ta2PdS5 nanowires. The superconducting critical field shows a strong anisotropic behavior and a violation of the Pauli limit in a parallel magnetic field configuration. Current-voltage measurements exhibit hysteresis loops and a series of multiple voltage steps in transition to the normal state, indicating a quasi-1D nature of the superconductivity. Surprisingly, the nanowire undergoes a superconductor-metal transition when the magnetic field increases. Upon approaching the zero-temperature quantum critical point, the system uncovers the signature of the quantum Griffiths singularity state arising from enhanced quenched disorders, where the dynamical critical exponent becomes diverging rather than being constant.

The three-state Potts antiferromagnet on plane quadrangulations

We study the antiferromagnetic 3-state Potts model on general (periodic) plane quadrangulations Γ. Any quadrangulation can be built from a dual pair (G,G*). Based on the duality properties of G, we propose a new criterion to predict the phase diagram of this model. If Γ is of self-dual type (i.e. if G is isomorphic to its dual G*), the model has a zero-temperature critical point with central charge c = 1, and it is disordered at all positive temperatures. If Γ is of non-self-dual type (i.e. if G is not isomorphic to G*), three ordered phases coexist at low temperature, and the model is disordered at high temperature. In addition, there is a finite-temperature critical point (separating these two phases) which belongs to the universality class of the ferromagnetic 3-state Potts model with central charge c = 4/5. We have checked these conjectures by studying four (resp. seven) quadrangulations of self-dual (resp. non-self-dual) type, and using three complementary high-precision techniques: Monte-Carlo simulations, transfer matrices, and critical polynomials. In all cases, we find agreement with the conjecture. We have also found that the Wang–Swendsen–Kotecký Monte Carlo algorithm does not have (resp. does have) critical slowing down at the corresponding critical point on quadrangulations of self-dual (resp. non-self-dual) type.

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations.

We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c=1. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

Localization of Interacting Dirac Fermions.

Using exact quantum MonteCarlo calculations, we examine the interplay between localization of electronic states driven by many-body correlations and that by randomness in a two-dimensional system featuring linearly vanishing density of states at the Fermi level. A novel disorder-induced nonmagnetic insulating phase is found to emerge from the zero-temperature quantum critical point separating a semimetal and a Mott insulator. Within this phase, a phase transition from a gapless Anderson-like insulator to a gapped Mott-like insulator is identified. Implications of the phase diagram are also discussed.

Non-Fermi liquids at finite temperature: Normal-state and infrared singularities

We analyze quantum criticality at finite temperature for a class of non-Fermi liquids with massless bosons. Finite temperature gives rise to new infrared singularities that invalidate standard perturbative treatments. We show how such divergences are resolved at a non-perturbative level, and obtain the resulting fermion self-energy. This leads to a new "thermal" non-Fermi liquid regime that extends over a wide range of frequencies, and which is absent from the zero temperature critical point. We analyze the resulting quantum critical region and properties of the retarded Green's function. More generally, such effects dominate in the nearly static limit and are expected to have a nontrivial impact on superconductivity and transport.

Ising Superconductivity and Quantum Phase Transition in Macro-Size Monolayer NbSe2

Two-dimensional (2D) transition metal dichalcogenides (TMDs) have a range of unique physics properties and could be used in the development of electronics, photonics, spintronics, and quantum computing devices. The mechanical exfoliation technique of microsize TMD flakes has attracted particular interest due to its simplicity and cost effectiveness. However, for most applications, large-area and high-quality films are preferred. Furthermore, when the thickness of crystalline films is down to the 2D limit (monolayer), exotic properties can be expected due to the quantum confinement and symmetry breaking. In this paper, we have successfully prepared macro-size atomically flat monolayer NbSe2 films on bilayer graphene terminated surface of 6H-SiC(0001) substrates by a molecular beam epitaxy (MBE) method. The films exhibit an onset superconducting critical transition temperature (Tconset) above 6 K and the zero resistance superconducting critical transition temperature (Tczero) up to 2.40 K. Simultaneously, the transport measurements at high magnetic fields and low temperatures reveal that the parallel characteristic field Bc//(T = 0) is above 5 times of the paramagnetic limiting field, consistent with Zeeman-protected Ising superconductivity mechanism. Besides, by ultralow temperature electrical transport measurements, the monolayer NbSe2 film shows the signature of quantum Griffiths singularity (QGS) when approaching the zero-temperature quantum critical point.

Phase competition and anomalous thermal evolution in high-temperature superconductors

The interplay of competing orders is relevant to high-temperature superconductivity known to emerge upon suppression of a parent antiferromagnetic order typically via charge doping. How such interplay evolves at low temperature---in particular at what doping level the zero-temperature quantum critical point (QCP) is located---is still elusive because it is masked by the superconducting state. The QCP had long been believed to follow a smooth extrapolation of the characteristic temperature $T^*$ for the strange normal state well above the superconducting transition temperature. However, recently the $T^*$ within the superconducting dome was reported to unexpectedly exhibit back-bending likely in the cuprate Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$. Here we show that the original and revised phase diagrams can be understood in terms of weak and moderate competitions, respectively, between superconductivity and a pseudogap state such as $d$-density-wave or spin-density-wave, based on both Ginzburg-Landau theory and the realistic $t$-$t^{\prime}$-$t^{\prime\prime}$-$J$-$V$ model for the cuprates. We further found that the calculated temperature and doping-level dependence of the quasiparticle spectral gap and Raman response qualitatively agrees with the experiments. In particular, the $T^*$ back-bending can provide a simple explanation of the observed anomalous two-step thermal evolution dominated by the superconducting gap and the pseudogap, respectively. Our results imply that the revised phase diagram is likely to take place in high-temperature superconductors.

Dynamic Magnetic Properties of the Spin-3/2 Ising Model on a Cylindrical Nanowire in an Oscillating Magnetic Field

Dynamic magnetic properties of the spin-3/2 model on a cylindrical nanowire in an oscillating magnetic field are investigated, within the mean-field theory, by utilizing Glauber-type stochastic dynamics. The thermal variations of the dynamic core, shell, and total magnetizations are examined and then dynamic phase diagrams are calculated in four different planes which exhibit several ordered and mixed phases, as well as dynamic tricritical and compensation behaviors. The double and zero-temperature critical points are also observed. Results are compared with the published works and find a quantitatively good agreement.

The dynamic critical properties of the spin-2 Ising model on a bilayer square lattice

The spin-2 Ising model is investigated for the ferromagnetic/ferromagnetic (FM/FM), antiferromagnetic/ferromagnetic (AFM/FM) and antiferromagnetic/antiferromagnetic (AFM/AFM) interactions on the two-layer square lattice by using the Glauber-type stochastic dynamics. The system is in contact with a heat bath at temperature T, and the exchange of energy with the heat bath occurs via one-spin flip. By employing the Master equation and Glauber transition rates, the dynamic equations of the system are obtained. These equations are solved by using the numerical methods. First, we investigate the average order parameters as a function of the time to find the phases in the system. Then, the temperature-dependence of the dynamic order parameters is examined to obtain the dynamic phase transition temperatures. The dynamic phase diagrams are presented on the different planes. According to the values of the system parameters, a variety of dynamic critical points such as tricritical point, triple point, quadruple point, critical end point, double critical end point, zero-temperature critical point, multicritical point and tetracritical point are obtained. The reentrant behavior is seen in the system for the AFM/AFM interaction. Finally, we also investigate the influence of the oscillating field frequency on the dynamic phase diagrams in detail.

Kinetic Transverse Ising Nanowire System in the Presence of a Time-Varying Magnetic Field

The dynamic phase diagrams of a kinetic transverse Ising nanowire system are investigated in the presence of a time-varying (sinusoidal) magnetic field [ h(t) = h0 sin(wt)] by using the effective-field theory based on Glauber-type stochastic dynamics. First, the time dependence of the magnetizations is studied in order to find the phases in the system. Then, the dynamic phase diagrams are presented in the (T, h), (T, r), and (T, ΔS) planes. It is found that the dynamic behavior of the system strongly depends on the values of the interaction parameters, and the different topological types of phase diagrams are obtained for the case of ferromagnetic and antiferromagnetic interactions. We observe the F, AF, and P fundamental phases and two mixed phases composed of binary combinations of the fundamental phases as well as a dynamic zero-temperature critical point and a multicritical point, depending on the interaction parameters. Moreover, the system also displays dynamic tricritical points, re-entrant behaviors as well as one and two compensation points.