Unusual Critical Behavior Research Articles

Characterization of gapless topological quantum phase transition via magnetocaloric effect

It has attracted much attention on the interplay between topology and criticality in topological quantum systems, i.e., gapless topological quantum phase transition (TQPT) on critical lines. It is demonstrated that the magnetocaloric effect (MCE) is able to signal the gapless TQPT in an extended Kitaev chain, which is witnessed by the unusual critical behavior of joint effect of Grüneison ration (GR) and isothermal entropy change. We uncover the conventional TQPT between gapped phases showing high symmetry (HS) and non-HS critical points with self-duality, which is signaled by the finite value of GR as T → 0 and the largest inverse MCE with T-linear relation of isothermal entropy change. Two critical lines intersect at a multicritical point, at which there is a T−1 critical divergence of GR as well as T1/2 critical behavior of isothermal entropy change. It manifests a “weak” gapless TQPT on one critical line, demonstrated by the shifting zero-crossing of GR without the largest inverse MCE. On the other critical line, it shows a “strong” gapless TQPT, which is evidenced by the negative dip of GR together with the largest inverse MCE. Our work provides a novel thermodynamic perspective on gapless TQPT.

Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model.

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

Unconventional critical behavior in a Sm-based ferromagnetic manganite : Effect of tricritical point

We have studied the critical phenomena in a single crystal of a ferromagnetic manganite (Sm1−xNdx)0.52Sr0.48 MnO3 with x = 0.6, which is in the vicinity of a tricritical point (x∗≈ 0.4), separating first-(x<0.4) from second-order (x>0.4) phase transition. Through magnetization scaling analysis, we have determined the critical exponents (β = 0.23 ± 0.01, γ = 1.30 ± 0.01, and δ = 6.63 ± 0.03) and critical amplitudes, which are also in accordance with the results obtained from the magnetic field dependence of magnetic entropy change. The exponents obey the scaling laws but they do not belong to any existing universality class − a clear violation of universality hypothesis. The occurrence of such unusual critical behavior has qualitatively been explained through mean-field theory, which reveals that for a system in the vicinity of tricritical point, the critical exponents may substantially differ from conventional universality.

Observation of unusual critical region behavior in the magnetic susceptibility of EuSe

The Europium Chalcogenides (EuCh: EuO, EuS, EuSe, and EuTe) have been regarded as model examples of simple, cubic, Heisenberg exchange coupled magnetic systems, with a ferromagnetic nearest-neighbor exchange constant J1 and an antiferromagnetic next-nearest-neighbor constant J2. Unlike the other EuCh, EuSe exhibits a range of complex magnetic behaviors, the latter being attributed to EuSe being near the point where J2=-J1, where its magnetism appears to consist of nearly de-coupled 2D ferromagnetic sheets. Analysis of precision SQUID measurements of the magnetic susceptibility χ in EuSe showed that in the region from ∼Tc to ∼2Tc, a fit of the data to the critical equation χ = χ2Tc(T/Tc-1)-γ gives γ=2.0, an exponent not predicted by any current theory. Additionally, this fit predicts that Tc should be ∼0K. We tentatively interpret this by saying that in the paramagnetic region the system "thinks" EuSe should not order above T=0. Tc=0K is predicted by the Mermin-Wagner theorem (MW) for Heisenberg-coupled 2D magnetic systems, and we can show that when J2=-J1, MW can also be applied to the J1, J2 exchange model of the EuCh to give a rigorous Tc=0 prediction. Under 10 kbar applied pressure EuSe exhibits a different γ and fitted Tc. An additional, and rather strange, critical-region effect was discovered. The EuSe sample was found to exhibit a relaxation effect in a small range of temperatures, just above and just below the actual Tc of 4.7K, with time constants of up to 5 minutes. We cannot yet fully explain this observed macroscopic effect.

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

The low-energy behaviors of gapless double- and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or $z$ component of random vector potential but exhibits stable critical behavior when there is only $x$ or $y$ component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and $x$, or $y$, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the $z$ component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double- and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered.

Multichain models of conserved lattice gas.

Conserved lattice-gas models in one dimension exhibit absorbing state phase transition (APT) with simple integer exponents β=1=ν=η, whereas the same on a ladder belong to directed percolation (DP) universality. We conjecture that additional stochasticity in particle transfer is a relevant perturbation and its presence on a ladder forces the APT to be in the DP class. To substantiate this we introduce a class of restricted conserved lattice-gas models on a multichain system (M×L square lattice with periodic boundary condition in both directions), where particles which have exactly one vacant neighbor are active and they move deterministically to the neighboring vacant site. We show that for odd number of chains, in the thermodynamic limit L→∞, these models exhibit APT at ρ_{c}=1/2(1+1/M) with β=1. On the other hand, for even-chain systems transition occurs at ρ_{c}=1/2 with β=1,2 for M=2,4, respectively, and β=3 for M≥6. We illustrate this unusual critical behavior analytically using a transfer-matrix method.

Subsolidus phase equilibria in the La2O3–Fe2O3–Sb2O5 system and characterization of layered ternary oxide LaFe0.5Sb1.5O6

Phase equilibria in the La2O3-Fe2O3–Sb2O5 system have been studied. The isothermal section was constructed at T=900°С. The existence of the ternary oxide LaFe0.5Sb1.5O6 was confirmed. The structure of this compound was solved using Rietveld refinement of synchrotron radiation-based powder XRD data. LaFe0.5Sb1.5O6 crystallizes in a trigonal layered structure relating to PbSb2O6 type (space group P-31m, a=b=5.2446(3)Å, c=5.1930(3)Å, Z=1). The fine powder of LaFe0.5Sb1.5O6 was prepared by molten salt synthesis. The compound was characterized by diffuse reflection and Mossbauer spectroscopy, magnetic measurements, scanning electron microscopy and photocatalytic tests. The magnetic behavior of LaFe0.5Sb1.5O6 in the applied magnetic field H=5000Oe is entirely paramagnetic. By contrast, in the small magnetic field H=100Oe the magnetic data of LaFe0.5Sb1.5O6 indicates an unusual critical behavior near phase transition at T<2K.

Unusual ferromagnetic critical behavior owing to short-range antiferromagnetic correlations in antiperovskite Cu(1-x)NMn(3+x) (0.1 ≤ x ≤ 0.4).

For ferromagnets, varying from simple metals to strongly correlated oxides,the critical behaviors near the Curie temperature (TC) can be grouped into several universal classes. In this paper, we report an unusual critical behavior in manganese nitrides Cu1-xNMn3+x (0.1 ≤ x ≤ 0.4). Although the critical behavior below TC can be well described by mean field (MF) theory, robust critical fluctuations beyond the expectations of any universal classes are observed above TC in x = 0.1. The critical fluctuations become weaker when x increases, and the MF-like critical behavior is finally restored at x = 0.4. In addition, the paramagnetic susceptibility of all the samples deviates from the Curie-Weiss (CW) law just above TC. This deviation is gradually smeared as x increases. The short-range antiferromagnetic ordering above TC revealed by our electron spin resonance measurement explains both the unusual critical behavior and the breakdown of the CW law.

Boson Pairing and Unusual Criticality in a GeneralizedXYModel

We discuss the unusual critical behavior of a generalized XY model containing both 2π-periodic and π-periodic couplings between sites, allowing for ordinary vortices and half-vortices. The phase diagram of this system includes both single-particle condensate and pair-condensate phases. Using a field theoretic formulation and worm algorithm MonteCarlo simulations, we show that in two dimensions it is possible for the system to pass directly from the disordered (high temperature) phase to the single particle (quasi)condensate via an Ising transition, a situation reminiscent of the "deconfined criticality" scenario.

Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids

The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.

Phase transition and critical properties of spin–orbital interacting systems

Abstract Phase transition and critical properties of Ising-like spin–orbital interacting systems in 2-dimensional triangular lattice are investigated. We first show that the ground state of the system is a composite spin–orbital ferro-ordered phase. Though Landau effective field theory predicts the second-order phase transition of the composite spin–orbital order, however, the critical exponents obtained by the renormalization group approach demonstrate that the spin–orbital order–disorder transition is far from the second-order, rather, it is more close to the first-order. The unusual critical behavior near the transition point is attributed to the fractionalization of the composite order parameter.

EFFECT OF FIELD DIRECTION AND FIELD INTENSITY ON DIRECTED SPIRAL PERCOLATION

Directed spiral percolation (DSP) is a new percolation model with crossed external bias fields. Since percolation is a model of disorder, the effect of external bias fields on the properties of disordered systems can be studied numerically using DSP. In DSP, the bias fields are an in-plane directional field (E) and a field of rotational nature (B) applied perpendicular to the plane of the lattice. The critical properties of DSP clusters are studied here varying the direction of E field and intensities of both E and B fields in two-dimensions. The system shows interesting and unusual critical behavior at the percolation threshold. Not only the DSP model is found to belong in a new universality class compared to that of other percolation models but also the universality class remains invariant under the variation of E field direction. Varying the intensities of the E and B fields, a crossover from DSP to other percolation models has been studied. A phase diagram of the percolation models is obtained as a function of intensities of the bias fields E and B.

Magnetic shielding properties of water in various molecular and molecular-ionic structures

1 H and 17 O magnetic shielding tensors of water molecules in various water clusters, as well as in waternpyridine H-bond complexes and in molecular-ionic structure of Br i (H2O)6 have been calculated using density functional theory. The full geometry optimization was performed in the framework of Becke’s three parameter hybrid method and the LeenYangnParr correlation functional (B3LYP) combined with 6-311++G** basis set. Magnetic shielding tensors have been calculated using the hybrid functional of Perdew, Burke, and Ernzerhof (PBE1PBE) and the gauge-including atomic orbital (GIAO) approach was applied to ensure gauge invariance of the results. Solvent effects were taken into account by polarizable continuum model (PCM). The calculated NMR parameters are compared with the corresponding experimental data for aqueous system, which exhibit an unusual critical behaviour and phase transitions.

Neutron diffraction and ESR studies of pseudocubic Nd 0.75Ba 0.25MnO 3 and its unusual critical behavior above [formula omitted

Results of structural neutron diffraction study and electron spin resonance (ESR) measurements are presented for insulating Nd 1− x Ba x MnO 3 ( x = 0.25 ) with the Curie temperature T C ≈ 129 K . Its pseudocubic structure reveals the definite distortions to a lower symmetry. Detailed analysis of the data is performed in the frame of Pbnm space group in a temperature range 4.2–300 K. The compound is found to exhibit the Jahn-Teller (JT) transition at T JT≈250 K. Character of the coherent JT distortions and their temperature evolution differ from those of the x = 0.23 manganite. The ESR results correspond to behavior of a 3D isotropic ferromagnet above T * ≈ 143 K ( τ * ≈ 0.12 ⩽ τ < 1 , τ = ( T – T C ) / T C ) . It is shown that an anisotropic exchange coupling of the Mn and Nd magnetic moments may give a substantial contribution in ESR linewidth masking its critical enhancement. The different temperature treatments (slow/fast cooling/heating with/without external magnetic field) of the sample reveal a temperature hysteresis of the ESR spectra below T* indicating an anomalous response in the paramagnetic region. The study of the magnetic phase transition in the x = 0.23 and 0.25 NdBa manganites suggests a change in its character from the second to first order at T*. The conventional free energy including the magnetization and magnetic field failed to describe this first-order transition. The unconventional critical behavior is attributed to an orbital liquid metallic phase that begins to coexist with the initial orbital-ordered phases below T*.

Absorbing phase transitions of unidirectionally coupled nonequilibrium systems

We investigate the change of critical behavior of two-level hierarchy systems in which the second level (B) is unidirectionally coupled to the first (A) by the coupling dynamics A --> A + nB with n = 1 or 2. The first level belongs to the directed percolation or the parity-conserving (PC) universality class, the second to PC. If both levels are critical, the active region of the second level becomes heterogeneous. In the so-called coupled region the first level feeds particles to the second, while in the uncoupled region the second level evolves autonomously. Measuring dynamic critical exponents in both regions, we show to what extent the critical behavior of the second level depends on the universality class of the first. These results suggest a simple criterion for the emergence of unusual critical behavior of unidirectionally coupled nonequilibrium systems.

Unusual critical behavior of the electrical resistivity near the first-order magnetostructural transition of Gd 5(Si 0.1Ge 0.9) 4

We report the temperature dependence of the electrical resistance ( R) of Gd 5(Si 0.1Ge 0.9) 4 near its (martensitic) magnetostructural transition at T S≏84 K, over different series of 10–300 K thermal cycles (>50). Large hysteresis is observed near T S, with a progressive change in the R( T) behavior and in the residual resistance upon thermal cycling. At intermediate number of cycles (∼13–28) a pre-martensitic phase occurs just below T S, with the remarkable property of displaying a universal R( T) behavior.

Parameter-free expression for superconducting T c in cuprates: BEC vs Kosterlitz-Thouless transition

A parameter-free expression for the superconducting critical temperature of layered cuprates is derived which allows us to express T c in terms of experimentally measured parameters. Remarkable agreement with the experiment as well as the unusual critical behaviour and the normal-state gap indicate that many cuprates are close to the Bose-Einstein condensation regime. Possibility of Kosterlitz-Thouless transition is discussed.

Parameter-free expression for superconductingTcin cuprates

A parameter-free expression for the superconducting critical temperature of layered cuprates is derived which allows us to express Tc in terms of experimentally measured parameters. It yields Tc values observed in about 30 lanthanum, yttrium and mercury-based samples for different levels of doping. This remarkable agreement with the experiment as well as the unusual critical behaviour and the normal-state gap indicate that many cuprates are close to the Bose-Einstein condensation regime.

Metal-Superconductor Transition at Zero Temperature: A Case of Unusual Scaling

An effective field theory is derived for the normal metal-to-superconductor quantum phase transition at T=0. The critical behavior is determined exactly for all dimensions d>2. Although the critical exponents \beta and \nu do not exist, the usual scaling relations, properly reinterpreted, still hold. A complete scaling description of the transition is given, and the physics underlying the unusual critical behavior is discussed. Quenched disorder leads to anomalously strong T_c-fluctuations which are shown to explain the experimentally observed broadening of the transition in low-T_c thin films.

Inhomogeneous systems with unusual critical behaviour

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are considered as well as general parabolic shapes. In the other case the system contains defects, either narrow ones in the form of lines or stars, or extended ones where the couplings deviate from their bulk values according to power laws. In each case the perturbation may be irrelevant, marginal or relevant. In the marginal case one finds local exponents which depend on a parameter. In the relevant case unusual stretched exponential behaviour and/or local first order transitions appear. The discussion combines mean field theory, scaling considerations, conformal transformations and perturbation theory. A number of examples are Ising models for which exact results can be obtained. Some walks and polymer problems are considered, too.