Order Parameter Susceptibility Research Articles

Calculation of the order parameter and dielectric susceptibility under the electric field near the incommensurate phase in NaNO2 using Landau model

ABSTRACT Temperature dependences of the order parameters (P and Ψ) and inverse susceptibilities (χp −1 and χΨ -1 ) are calculated for the ferroelectric(FE)-incommensurate (INC) – paraelectric (PE) transitions in NaNO2 at zero (E = 0) and constant electric fields E by the Landau phenomenological model. For the calculation of the polarisation P and the order parameter Ψ, the phase line equations are fitted to the observed data (E = 0) from the literature. On this basis, E-T phase diagram including the ferroelectric, incommensurate and paraelectric phases is constructed using the observed (E-T) data for NaNO2 as reported in the literature. In the presence of the polarisation P (secondary order parameter), which has a biquadratic coupling with the Ψ (primary order parameter) in the incommensurate phase, the Landau model presented here describes the observed behaviour of the FE-INC and INC-PE transitions in NaNO2. Under constant electric fields, our predictions can be compared with the experiments. This method of calculation can be applied to some other crystals exhibiting the incommensurate phase between the FE and PE phases.

Biswas-Chatterjee-Sen Model on Solomon Networks with Two Three-Dimensional Lattices.

The Biswas-Chatterjee-Sen (BChS) model of opinion dynamics has been studied on three-dimensional Solomon networks by means of extensive Monte Carlo simulations. Finite-size scaling relations for different lattice sizes have been used in order to obtain the relevant quantities of the system in the thermodynamic limit. From the simulation data it is clear that the BChS model undergoes a second-order phase transition. At the transition point, the critical exponents describing the behavior of the order parameter, the corresponding order parameter susceptibility, and the correlation length, have been evaluated. From the values obtained for these critical exponents one can confidently conclude that the BChS model in three dimensions is in a different universality class to the respective model defined on one- and two-dimensional Solomon networks, as well as in a different universality class as the usual Ising model on the same networks.

Marginal Fermi liquid behavior at the onset of 2kF density wave order in two-dimensional metals with flat hot spots

We analyze quantum fluctuation effects at the onset of incommensurate 2kF charge- or spin-density-wave order in two-dimensional metals for a model in which the ordering wave vector Q connects a single pair of hot spots on the Fermi surface with a vanishing Fermi surface curvature. The tangential momentum dependence of the bare dispersion near the hot spots is proportional to |kt|α with α>2. We first compute the order parameter susceptibility and the fermion self-energy in a random phase approximation (RPA). Logarithmic divergences are subsequently treated by a renormalization-group analysis. The coupling between the order parameter fluctuations and the fermions vanishes logarithmically in the low-energy limit. As a consequence, the logarithmic divergences found in the RPA do not sum up to anomalous power laws. Instead, only logarithmic corrections to Fermi liquid behavior are obtained. In particular, the quasiparticle weight and the Fermi velocity vanish logarithmically at the hot spots. Published by the American Physical Society 2024

Microscopic pathways of transition from low-density to high-density amorphous phase of water.

In recent years, much attention has been devoted to understanding the pathways of phase transition between two equilibrium condensed phases (such as liquids and solids). However, the microscopic pathways of transition involving non-equilibrium, non-diffusive amorphous (glassy) phases still remain poorly understood. In this work, we have employed computer simulations, persistence homology (a tool rooted in topological data analysis), and machine learning to probe the microscopic pathway of pressure-induced non-equilibrium transition between the low- and high-density amorphous (LDA and HDA, respectively) ice phases of the TIP4P/2005 and ST2 water models. Using persistence homology and machine learning, we introduced a new order parameter that unambiguously identifies the LDA- and HDA-like local environments. The LDA phase transitions continuously and collectively into the corresponding HDA phase via a pre-ordered intermediate phase during the isothermal compression. The local order parameter susceptibilities show a maximum near the transition pressure (P*)-suggesting maximum structural heterogeneities near P*. The HDA-like clusters are structurally ramified and spatially delocalized inside the LDA phase near the transition pressure. We also found manifestations of the first-order low-density to high-density liquid transition in the sharpness of the order parameter change during the LDA to HDA transition. We further investigated the (geometrical) structures and topologies of the LDA and HDA ices formed via different protocols and also studied the dependence of the (microscopic) pathway of phase transition on the protocol followed to prepare the initial LDA phase. Finally, the method adopted here to study the phase transition pathways is not restricted to the system under consideration and provides a robust way of probing phase transition pathways involving any two condensed phases at both equilibrium and out-of-equilibrium conditions.

Non-Fermi liquid behavior at flat hot spots from quantum critical fluctuations at the onset of charge- or spin-density wave order

We analyze quantum fluctuation effects at the onset of charge- or spin-density wave order with a $2{k}_{F}$ wave vector $\mathbf{Q}$ in two-dimensional metals, for the special case where $\mathbf{Q}$ connects a pair of hot spots situated at high symmetry points of the Fermi surface with a vanishing Fermi surface curvature. We compute the order parameter susceptibility and the fermion self-energy in one-loop approximation. The susceptibility has a pronounced peak at $\mathbf{Q}$, and the self-energy displays non-Fermi liquid behavior at the hot spots, with a linear frequency dependence of its imaginary part. The real part of the one-loop self-energy exhibits logarithmic divergencies with universal prefactors as a function of both frequency and momentum, which may be interpreted as perturbative signatures of power laws with universal anomalous dimensions. As a result, one obtains a non-Fermi liquid metal with a vanishing quasiparticle weight at the hot spots, and a renormalized dispersion relation with anomalous algebraic momentum dependencies near the hot spots.

Chiral phase structure of three flavor QCD in a background magnetic field

We investigate the chiral phase structure of three flavor QCD in a background $U(1)$ magnetic field using the standard staggered action and the Wilson plaquette gauge action. We perform simulations on lattices with a temporal extent of $N_\tau=4$ and four spatial extents of $N_\sigma = 8,16, 20$ and 24. We choose a smaller-than-physical quark mass in lattice spacing as $am = 0.030$ such that there exists a crossover transition at vanishing magnetic fields, and adopt two values of magnetic field strength in lattice spacing $a \sqrt{ e{B}}\simeq 1.5$ and 2. We find that the transition becomes stronger in the presence of a background magnetic field, and turns into a first order as seen from the volume scaling of the order parameter susceptibility as well as the metastable states in the time history of the chiral condensate. On the other hand, the chiral condensate and transition temperature always increase with $B$ even within the regime of a first order phase transition. This suggests that the discrepancy in the behavior of chiral condensates and transition temperature as a function of $B$ between earlier lattice studies using larger-than-physical pion masses with standard staggered fermions and those using physical pions with improved staggered fermions is mainly due to lattice cutoff effects.

Temperature dependence of magnetic and thermal properties of chiral HyFe and HyMn close to phase transitions by using the Landau mean field model

Abstract Magnetic and thermal properties of chiral metal formate frameworks (MOFs) of NH2NH3M(HCOO)3, M = Fe, Mn, namely, HyFe and HyMn are investigated close to phase transitions by using Landau phenomenological model. By expanding the free energy in terms of the order parameter, for magnetic properties the temperature dependence of magnetization and inverse magnetic susceptibility, and for thermal properties the heat capacity and entropy are calculated for chiral HyFe and HyMn close to phase transitions using the experimental data from the literature. Additionally, structural order parameter and inverse susceptibility are predicted from the model, which can be compared with the observed data for chiral HyFe and HyMn. It is found that Landau phenomenological model is adequate to describe the phase transitions in chiral HyFe, and antiferromagnet chiral HyMn.

Monte Carlo simulations of a disordered superconductor-metal quantum phase transition

We investigate the quantum phase transitions of a disordered nanowire from superconducting to metallic behavior by employing extensive Monte Carlo simulations. To this end, we map the quantum action onto a (1+1)-dimensional classical XY model with long-range interactions in imaginary time. We then analyze the finite-size scaling behavior of the order parameter susceptibility, the correlation time, the superfluid density, and the compressibility. We find strong numerical evidence for the critical behavior to be of infinite-randomness type and to belong to the random transverse-field Ising universality class, as predicted by a recent strong disorder renormalization group calculation.

Density functional and Monte Carlo investigation of FeNi/MoS2 junction

In this paper, first principles computations are performed to investigate structural, electronic, magnetic, and thermodynamic properties of a novel two-dimensional ferromagnet/semiconductor junction, consisting of a monolayer of FeNi on a single monolayer of ${\mathrm{MoS}}_{2}$. After investigating more than 30 different arrangements of Fe and Ni atoms on ${\mathrm{MoS}}_{2}$, it is concluded that Ni-S bonding is more likely at the FeNi/${\mathrm{MoS}}_{2}$ interface, while highly spin polarized Fe atoms prefer to stay well above the ${\mathrm{MoS}}_{2}$ monolayer, forming a zigzag FeNi layer at the surface. Accurate investigation of the electronic structure of the most stable configuration of FeNi/${\mathrm{MoS}}_{2}$ junction evidences appearance of some majority and minority surface charge carriers with very different mobilities, predicting a high spin polarized conductivity in the junction. Tens of different spin orderings are applied to the FeNi monolayer in a $3\ifmmode\times\else\texttimes\fi{}3$ supercell to achieve reliable Heisenberg exchange constants for parametrization of the magnetic energy of the FeNi/${\mathrm{MoS}}_{2}$ junction. The obtained exchange constants are then used for classical Monte Carlo simulation of magnetic thermodynamic properties of the system, including magnetic order parameter, heat capacity, and magnetic susceptibility. The predicted very high paramagnetic transition temperature ($g1300\phantom{\rule{0.28em}{0ex}}\text{K}$) along with the speculated high spin polarized conductivity evidences potential application of this junction in spintronics.

خواص مغناطیسی عایقهای توپولوژیکی مغناطیسی سه بعدی:اثرات انحنای شش گوشی

We have investigated the magnetic properties of three-dimensional topological insulators, doped with magnetic atoms. The spin-orbit locking of surface electrons results in interesting magnetic behaviors, absent in conventional insulators without spin-orbit coupling. In particular, the ferromagnetic-paramagnetic transition temperature has a strong dependence on different system parameters. Here, using the mean-field formalism we have studied the effects of hexagonal warping on the order parameter, critical temperature, and magnetic susceptibility of system.

Correlations between the resonant frequency shifts and the thermodynamic quantities for the α-β transition in quartz

The resonant frequency shifts are related to the thermodynamic quantities (compressibility, order parameter and susceptibility) for the α-β transition in quartz. The experimental data for the resonant frequencies and the bulk modulus from the literature are used for those correlations. By calculating the order parameter from the mean field theory, correlation between the resonant frequencies of various modes and the order parameter is examined according to the quasi-harmonic phonon theory for the α-β transition in quartz. Also, correlation between the bulk modulus in relation to the resonant frequency shifts and the order parameter susceptibility is constructed for the α-β transition in this crystalline system.

Analysis of the susceptibility in a fluid system with Neumann – plus boundary conditions

The behaviour of the local and total susceptibilities of a fluid system bounded by different surfaces is studied in the framework of the Ginsburg-Landau Ising type model. The case of a plain geometry, Neumann-infinity boundary conditions under variations of the temperature and an external ordering field is considered. Exact analytic expressions for the order parameter, local and total susceptibilities in such a system are presented. They are used to analyse the phase behaviour of fluids confined in regions close to the bulk critical point of the respective infinite system.

Frequency Variation of the AC Order Parameter Susceptibility of the Metamagnetic Ising Model

The extensive investigation of the absorptive and reactive parts of the AC order parameter susceptibility spectra of iron group dihalides, which is obtained on the basis of Onsager theory of irreversible processes, revealed the fact that the diagonal phenomenological rate coefficients γs and γm have an important impact on the nature of the order parameter relaxation process. The number of the relaxation peaks appearing in the double logarithmic plots of χs′′ versus field frequency ω and the number of plateau regions in χs′ spectrum depends on the values of γs and γm. Only for γs≫γm does the relaxation evolve from a simple Debye exponential at high temperatures to a two-step process at lower temperatures in which there exist two long relaxation times characterizing the relaxation of staggered magnetization. In parallel with these characteristics of the order parameter relaxation, Cole-Cole plots (χs′′-χs′) are shown to consist of two arcs in the metamagnetic phase and of a semicircle in the paramagnetic phase.

Strong coupling phases of the spin-orbit-coupled spin-1 Bose-Hubbard chain: odd integer Mott lobes and helical magnetic phases.

We study the odd integer filled Mott phases of a spin-1 Bose-Hubbard chain and determine their fate in the presence of a Raman induced spin-orbit coupling which has been achieved in ultracold atomic gases; this system is described by a quantum spin-1 chain with a spiral magnetic field. The spiral magnetic field initially induces helical order with either ferromagnetic or dimer order parameters, giving rise to a spiral paramagnet at large field. The spiral ferromagnet-to-paramagnet phase transition is in a novel universality class, with critical exponents associated with the divergence of the correlation length and the order parameter susceptibility . We solve the effective spin model exactly using the density matrix renormalization group, and compare with both a large- classical solution and a phenomenological Landau theory. We discuss how these exotic bosonic magnetic phases can be produced and probed in ultracold atomic experiments in optical lattices.

Soft-mode spectroscopy in cubic (Ba 0.8 Sr 0.2 )Ti 0.95 (Zn 1/3 Nb 2/3 ) 0.05 O 3 by hyper-Raman scattering and the mechanism of the phase transition

Abstract This paper presents a survey of soft modes and their relationship to structural phase transitions. After introducing the concept of a soft mode, the origin of softening is considered from a lattice-dynamical point. The Landau theory approach to structural transitions is then discussed, followed by a generalization of the soft-mode concept through the use of the dynamic order-parameter susceptibility. The hyper-Raman spectra in the cubic phase of (Ba0.8Sr0.2)Ti0.95(Zn1/3Nb2/3)0.05O3 are studied with special emphasis on the lowest-frequency phonon mode. The spectral structure is found to change above the Curie temperature (303–873 K). Soft modes were put forward by Cochran and Anderson about 50 years ago as an explanation of structural phase transitions. Extending Landau's theory of phase transitions, their prediction was that the square of the frequency of the soft mode was proportional to ω 0 ( T ) = C T − T C where Tc is the transition temperature.

Frustrated Heisenberg antiferromagnet on the honeycomb lattice with spin quantum number s ≥ 1

The ground-state (GS) phase diagram of the frustrated spin-s J1-J2-J3 Heisenberg antiferromagnet on the honeycomb lattice is studied using the coupled cluster method implemented to high orders of approximation, for spin quantum numbers s = 1, 3/2, 2 , 5/2. The model has antiferromagnetic (AFM) nearest-neighbour, next-nearest-neighbour and next-next-nearest-neighbour exchange couplings (with strength J1 > 0, J2 > 0 and J3 > 0, respectively). We specifically study the case J3 = J2 = κJ1, in the range 0 < κ < 1 of the frustration parameter, which includes the point of maximum classical (s → ∞) frustration, viz., the classical critical point at κcl = 1/2, which separates the Neel phase for κ < κcl and the collinear striped AFM phase for κ > κcl. Results are presented for the GS energy, magnetic order parameter and plaquette valence-bond crystal (PVBC) susceptibility. For all spins s > 3/2 we find a quantum phase diagram very similar to the classical one, with a direct first-order transition between the two collinear AFM states at a value κc(s) which is slightly greater than κcl [e.g., κc(3/2) ≈ 0.53(1)] and which approaches it monotonically as s → ∞. By contrast, for the case s = 1 the transition is split into two such that the stable GS phases are one with Néel AFM order for κ < κc1 = 0.485(5) and one with striped AFM order for κ > κc2 = 0.528(5), just as in the case s = 1/2 (for which κc1 ≈ 0.47 and κc2 ≈ 0.60). For both the s = 1/2 and s = 1 models the transition at κc2 appears to be of first-order type, while that at κc1 appears to be continuous. However, whereas in the s = 1/2 case the intermediate phase appears to have PVBC order over the entire range κc1 < κ < κc2, in the s = 1 case PVBC ordering either exists only over a very small part of the region or, more likely, is absent everywhere.

Monte Carlo study of the Spin-1 Baxter-Wu model in a crystal field

The two-dimensional Baxter-Wu model with spin-1, in the presence of a crystal field, is studied by using Monte Carlo simulations. The standard single-spin-flip Metropolis algorithm is used to generate the configurations from which the order parameter, specific heat and magnetic susceptibility are measured. Single histogram techniques are used to get the results close to the phase transitions. The finite-size scaling procedure is employed in order to obtain the critical behavior. The simulations have shown that the critical exponents are different from the spin-1/2 case and are crystal field dependent.

Constraining quantum critical dynamics: (2+1)D Ising model and beyond.

Quantum critical (QC) phase transitions generally lead to the absence of quasiparticles. The resulting correlated quantum fluid, when thermally excited, displays rich universal dynamics. We establish nonperturbative constraints on the linear-response dynamics of conformal QC systems at finite temperature, in spatial dimensions above 1. Specifically, we analyze the large frequency or momentum asymptotics of observables, which we use to derive powerful sum rules and inequalities. The general results are applied to the O(N) Wilson-Fisher fixed point, describing the QC Ising model when N=1. We focus on the order parameter and scalar susceptibilities, and the dynamical shear viscosity. Connections to simulations, experiments, and gauge theories are made.

Evidence of a short-range incommensurate [formula omitted]-wave charge order from a fermionic two-loop renormalization group calculation of a 2D model with hot spots

The two-loop renormalization group (RG) calculation is considerably extended here for the two-dimensional (2D) fermionic effective field theory model, which includes only the so-called “hot spots” that are connected by the spin-density-wave (SDW) ordering wavevector on a Fermi surface generated by the 2D t−t′ Hubbard model at low hole doping. We compute the Callan–Symanzik RG equation up to two loops describing the flow of the single-particle Green’s function, the corresponding spectral function, the Fermi velocity, and some of the most important order-parameter susceptibilities in the model at lower energies. As a result, we establish that–in addition to clearly dominant SDW correlations–an approximate (pseudospin) symmetry relating a short-range incommensurated-wave charge order to the d-wave superconducting order indeed emerges at lower energy scales, which is in agreement with recent works available in the literature addressing the 2D spin-fermion model. We derive implications of this possible electronic phase in the ongoing attempt to describe the phenomenology of the pseudogap regime in underdoped cuprates.

Order parameter, correlation functions, and fidelity susceptibility for the BCS model in the thermodynamic limit

The exact ground state of the reduced BCS Hamiltonian is investigated numerically for large system sizes and compared with the BCS ansatz. A ``canonical'' order parameter is found to be equal to the largest eigenvalue of Yang's reduced density matrix in the thermodynamic limit. Moreover, the limiting values of the exact analysis agree with those obtained for the BCS ground state. Exact results for the ground-state energy, level occupations, and a pseudospin-pseudospin correlation function are also found to converge to the BCS values already for relatively small system sizes. However, discrepancies persist for a pair-pair correlation function, for interlevel correlations of occupancies and for the fidelity susceptibility, even for large system sizes where these quantities have visibly converged to well-defined limits. Our results indicate that there exist nonperturbative corrections to the BCS predictions in the thermodynamic limit.