Susceptibility Exponent Research Articles

STUDY OF EXTRAORDINARY PHASE TRANSITION IN THIN ANTI-FERROMAGNETIC FILMS: COMPUTER SIMULATION

In the article, an extraordinary phase transition in thin antiferromagnetic films was investigated by computer modeling. The simulation uses the Ising model and Metropolis algorithm. Cubic crystal lattice epitaxial films containing multiple monoatomic layers are studied in the paper. The difference in the value for the exchange integrals in the bulk and on the surface of the film is a condition for the appearance of surface and extraordinary phase transitions. The film shall contain at least eight monoatomic layers for appearance of surface and extraordinary phase transitions. The extraordinary phase transition is investigated at different film thicknesses. Magnetic susceptibility demonstrates a logarithmic dependence on Neel temperature near the phase transition point. The dependence of the critical exponent of magnetic susceptibility on film thickness is calculated for the logarithmic phase.

Observation of griffiths phase and ferromagnetism in LaFe0.5Mn0.5O3

We report the structural and magnetic characterization of the polycrystalline LaFe0.5Mn0.5O3 compound. It crystallizes in an orthorhombic crystal structure with Pnma space group. A systematic investigation of magnetic behavior revealed the antiferromagnetic ordering at 276 K and Griffiths Phase-like behavior in the temperature range of 276 K to 314 K, confirmed by the power-law susceptibility exponent(λ). At a low temperature, spontaneous magnetization (Ms) is due to dominant ferromagnetic interaction. We estimated the magnitude using Arrot plot of different isotherms.

Phase transitions in an ordered 2D array of cubic nanoparticles

The study of phase transitions in an ordered cubic nanoparticles 2D array was carried out by computer modeling. The study was performed for the Ising model. The Wolf cluster algorithm is used to simulate the phase transition in the system. The interaction between the nanoparticles is exchange. The interaction between spins for different particles is less in one particle. Cases of different energy values for the interaction between particles are considered. The particles are single-domain. The ferromagnetic phase transition is investigated. The total magnetization in the system is used as an order parameter. The phase transition temperature is calculated based on finite dimensional scaling theory using Binder cummulants. A computer experiment was performed. The phase transition temperature dependence on energy of interaction between particles is obtained. The temperature changes according to the logarithmic law. The parameters for the Curie temperature change law from the interaction energy of nanoparticles are calculated. Critical exponents of the system were calculated. The critical exponents are independent from the interaction energy between the particles. The critical exponent for magnetic susceptibility is equal γ = 2.21± 0.09. This value is different from the critical exponents for a solid film.

Critical properties of the Néel–algebraic-spin-liquid transition

The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to (2+1)D quantum electrodynamics (QED$_3$), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $\pi$-flux phase, originally proposed as a possible ground state of the spin-1/2 Heisenberg model on the 2D square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-1/2 fermions coupled to a compact U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy N\'eel order and drive a direct quantum phase transition to the $\pi$-flux phase. We show this transition is in the universality class of the chiral Heisenberg QED$_3$-Gross-Neveu-Yukawa model with a single SU(2) doublet of four-component Dirac fermions (i.e., $N_f=1$), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $\epsilon$ expansion below four spacetime dimensions to four-loop order, and a large-$N_f$ expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a byproduct of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-N\'eel transition for interacting fermions on the honeycomb lattice.

Exact analysis of phase transitions in mean-field Potts models.

We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free energy, in the thermodynamic limit, follows from its semiclassical limit. Analysis of singularities of the equations of state reveals the occurrence of phase transitions of nematic type at not zero external fields and allows for an interpretation of the phase transitions in terms of shock dynamics in the space of thermodynamic variables. The approach is shown at work in the case of a q-state model for q=3 but the method generalizes to arbitrary q. Critical asymptotics of magnetization, susceptibility, specific heat and relative critical exponents β,γ, and α are also provided.

Bose-Fermi Anderson model with SU(2) symmetry: Continuous-time quantum Monte Carlo study

In quantum critical heavy fermion systems, local moments are coupled to both collective spin fluctuations and conduction electrons. As such, the Bose-Fermi Kondo model, describing the coupling of a local moment to both a bosonic and a fermionic bath, has been of extensive interest. For the model in the presence of SU(2) spin rotational symmetry, questions have been raised about its phase diagram. Here we develop a version of continuous-time Quantum Monte Carlo (CT-QMC) method suitable for addressing this issue; this procedure can reach sufficiently low temperatures while preserving the SU(2) symmetry. Using this method for the Bose-Fermi Anderson model, we clarify the renormalization-group fixed points and the phase diagram for the case with a constant fermionic-bath density of states and a power-law bosonic-bath spectral function $\rho_{b}(\omega) \propto \omega^{s}$ ($0<s<1$). We find two types of Kondo destruction QCP, depending on the power-law exponent $s$ in the bosonic bath spectrum. For $s^{*}<s<1$, both types of QCPs exist and, in the parameter regime accessible by an analytical $\epsilon$-expansion renormalization-group calculation (here $\epsilon=1-s$), the CT-QMC result is fully consistent with prior predictions by the latter method. For $s<s^{*}$, there is only one type of QCP. At both type of Kondo destruction QCPs, we find that the exponent of the local spin susceptibility $\eta$ obeys the relation $\eta=\epsilon$, which has important implications for Kondo destruction QCP in the Kondo lattice problem.

Magnetocaloric effect and critical behaviour of La0.5Ca0.2Ag0.3MnO3 compound

We present a dc magnetization study of the critical phenomena of a manganite oxide La0.5Ca0.2Ag0.3MnO3 single crystal. Based on the assumption of a continuous (second order) manganite transition for our sample, we have determined the critical temperature Tc = 264 K and the critical exponents β=0.18259±0.004 (β: critical exponent for the temperature dependence of spontaneous magnetization just below TC), γ=0.81967±0.0.029 (γ: critical exponent for the inverse initial susceptibility just above TC) and δ=5.45±0.006 (δ: critical exponent for the Widom scaling relation (T = TC)). From the field dependence of the magnetic entropy ΔSMΔSM∝Hn and the relative cooling power (RCP) RCP∝H∧1+1/δ, it was possible to evaluate the critical exponents of the magnetic phase transitions. Their values are in good agreement with those obtained from the critical exponents using a modified Arrott method.

Spin Seebeck Effect from Antiferromagnetic Magnons and Critical Spin Fluctuations in Epitaxial FeF_{2} Films.

We report a longitudinal spin Seebeck effect (SSE) study in epitaxially grown FeF_{2}(110) antiferromagnetic (AFM) thin films with strong uniaxial anisotropy over the temperature range of 3.8-250K. Both the magnetic-field and temperature-dependent SSE signals below the Néel temperature (T_{N}=70 K) of the FeF_{2} films are consistent with a theoretical model based on the excitations of AFM magnons without any net induced static magnetic moment. In addition to the characteristic low-temperature SSE peak associated with the AFM magnons, there is another SSE peak at T_{N} which extends well into the paramagnetic phase. All the SSE data taken at different magnetic fields up to 12T near and above the critical point T_{N} follow the critical scaling law very well with the critical exponents for magnetic susceptibility of 3D Ising systems, which suggests that the AFM spin correlation is responsible for the observed SSE near T_{N}.

Disordered Ising model with correlated frustration

We consider the J Ising model on a cubic lattice with a gauge-invariant disorder distribution. Disorder depends on a parameter that plays the role of a chemical potential for the amount of frustration. We study the model at a specific value of the disorder parameter , where frustration shows long-range correlations. We characterize the universality class, obtaining accurate estimates of the critical exponents: and , where is the overlap susceptibility exponent.

Critical properties of the quasi-two-dimensional metallic ferromagnet Fe2.85GeTe2

We have investigated the critical behavior of Fe2.85GeTe2 single crystals near the paramagnetic-ferromagnetic transition by bulk dc magnetization measurements. The critical exponents β, γ and δ, obtained from modified Arrott plot, Kouvel–Fisher method, and critical isothermal magnetization analysis, could fulfill the Widom scaling law. The self-consistency and reliability of these exponents are further verified by the magnetic state equations below and above the Curie temperature at high magnetic field. In addition, the exchange distance deduced from the susceptibility exponent is shown to decay as . Based on the observations, we suggest that the competition between direct magnetic exchange and Coulombic and/or RKKY interactions should be responsible for the intrinsic magnetism in this system.

Susceptibility Critical Exponent of a 1D Ising Ring-Type Ferromagnetic

Using the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН3)3NH] · FeCl3 · 2H2O and with the magnitude of the exchange interaction J/kB = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown that values of the susceptibility exponent for the one-dimensional Ising model with periodic boundary conditions are considerably less than the known values of the exponents for three-dimensional systems. The critical susceptibility exponent strongly depends on energy parameters; namely, it decreases with an increase in them.

Polysulfobetaines in Aqueous Solution and in Thin Film Geometry.

Polysulfobetaines in aqueous solution show upper critical solution temperature (UCST) behavior. We investigate here the representative of this class of materials, poly (N,N-dimethyl-N-(3-methacrylamidopropyl) ammonio propane sulfonate) (PSPP), with respect to: (i) the dynamics in aqueous solution above the cloud point as function of NaBr concentration; and (ii) the swelling behavior of thin films in water vapor as function of the initial film thickness. For PSPP solutions with a concentration of 5 wt.%, the temperature dependence of the intensity autocorrelation functions is measured with dynamic light scattering as function of molar mass and NaBr concentration (0–8 mM). We found a scaling of behavior for the scattered intensity and dynamic correlation length. The resulting spinodal temperatures showed a maximum at a certain (small) NaBr concentration, which is similar to the behavior of the cloud points measured previously by turbidimetry. The critical exponent of susceptibility depends on NaBr concentration, with a minimum value where the spinodal temperature is maximum and a trend towards the mean-field value of unity with increasing NaBr concentration. In contrast, the critical exponent of the correlation length does not depend on NaBr concentration and is lower than the value of 0.5 predicted by mean-field theory. For PSPP thin films, the swelling behavior was found to depend on film thickness. A film thickness of about 100 nm turns out to be the optimum thickness needed to obtain fast hydration with H2O.

Linked cluster expansions for open quantum systems on a lattice

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Pad\'e analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.

Критический индекс восприимчивости 1D-изинговского ферромагнетика, замкнутого в кольцо

AbstractUsing the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН_3)_3NH] · FeCl_3 · 2H_2O and with the magnitude of the exchange interaction J/k _B = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown that values of the susceptibility exponent for the one-dimensional Ising model with periodic boundary conditions are considerably less than the known values of the exponents for three-dimensional systems. The critical susceptibility exponent strongly depends on energy parameters; namely, it decreases with an increase in them.

Finite-size behaviour of generalized susceptibilities in the whole phase plane of the Potts model**Supported by Fund Project of National Natural Science Foundation of China (11647093, 11405088, 11521064), Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University (2016RC004) and the Major State Basic Research Development Program of China (2014CB845402)

We study the sign distribution of generalized magnetic susceptibilities in the temperature-external magnetic field plane using the three-dimensional three-state Potts model. We find that the sign of odd-order susceptibility is opposite in the symmetric (disorder) and broken (order) phases, but that of the even-order one remains positive when it is far away from the phase boundary. When the critical point is approached from the crossover side, negative fourth-order magnetic susceptibility is observable. It is also demonstrated that non-monotonic behavior occurs in the temperature dependence of the generalized susceptibilities of the energy. The finite-size scaling behavior of the specific heat in this model is mainly controlled by the critical exponent of the magnetic susceptibility in the three-dimensional Ising universality class.

Structural characterization, magnetic, magnetocaloric properties and critical behavior in lacunar La0.5Eu0.2Ba0.2□0.1MnO3 nanoparticles

The lacunar La0.5Eu0.2Ba0.2□0.1MnO3 nanoparticles where □ is a barium deficiency has been prepared using the sol-gel method. The M-T data suggests that the sample undergoes a paramagnetic (PM) to ferromagnetic (FM) transition upon cooling. Deviation of the temperature dependence of inverse susceptibility curves from the Curie Weiss law and less than unity susceptibility exponents indicating the existence of a Griffiths singularity. The magnetocaloric effect and the critical behavior of the sample are systematically studied using bulk magnetization M (H, T) in the vicinity of the Curie temperature. The critical exponents have been obtained using different methods such as modified Arrott plot, critical isotherm analysis and field dependence of magnetocaloric effect. Though the self-consistency and reliability of obtained critical exponents of β = 0.581 ± 0.022, γ = 0.165 ± 0.008 and δ = 3.12 ± 0.03 are verified by the Widom scaling law and scaling equations, the critical parameters do not obey magnetocaloric effect scaling laws, indicating that the nanometer size effect play a significant role on the magnetic phase transition for La0.5Eu0.2Ba0.2□0.1MnO3 nanocrystalline.

Two-dimensional percolation transition in two atomic layers of Fe on W(110): Direct measurement of a static percolation critical exponent in a two-dimensional Ising system

When the coverage of the second atomic layer of Fe in an Fe/W(110) ultrathin film reaches a critical value, the system moves suddenly from a frustrated magnetic state without long-range order to an in-plane ferromagnetic state with long-range order, and displays many features of a percolation transition. Measurements of the magnetic susceptibility as the films are grown at 255 K show power law scaling that is limited by noise at low deposition, and by the dynamics of the paramagnetic, frustrated state at high deposition. Because the measurements represent a system driven by a finite field oscillating at a finite frequency, it is demonstated that the threshold deposition for percolation is bounded by the depositions where the real and imaginary components of the susceptibility have maxima. Fitting for the critical exponent of the static susceptibility at these bounds gives a bounded value for $\gamma_p=2.39\pm0.04$, in agreement with theory.

Critical behavior of dissipative two-dimensional spin lattices

We explore critical properties of two-dimensional lattices of spins interacting via an anisotropic Heisenberg Hamiltonian and subject to incoherent spin flips. We determine the steady-state solution of the master equation for the density matrix via the corner-space renormalization method. We investigate the finite-size scaling and critical exponent of the magnetic linear susceptibility associated to a dissipative ferromagnetic transition. We show that the Von Neumann entropy increases across the critical point, revealing a strongly mixed character of the ferromagnetic phase. Entanglement is witnessed by the quantum Fisher information which exhibits a critical behavior at the transition point, showing that quantum correlations play a crucial role in the transition even though the system is in a mixed state.

Isotropic-Heisenberg to isotropic-dipolar crossover and finite-size scaling in Cr75−xFe25+x (x = 0, 5) thin films

‘Zero-field’ linear ac magnetic susceptibility, χ1(T), of the Cr75−xFe25+x (x=0, 5) thin films with thickness, t, ranging from 980 to 10nm has been measured at temperatures close to Tc, the temperature at which the ferromagnetic-paramagnetic phase transition occurs. An elaborate analysis of χ1(T⩾Tc) for the films with t⩾40nm yields the temperature dependence of the effective critical exponent for susceptibility, γeff(T), that is characteristic of the three-dimensional (3D) isotropic Heisenberg-to-3D isotropic dipolar crossover. In the asymptotic critical region (ACR), these thin-film samples behave as a 3D isotropic dipolar (ID) ferromagnet. As the film thickness reduces from t≃ 980nm to 40nm, ACR narrows down while the temperature, Tdip, at which a dip in γeff(T) occurs and the temperature, TIH∗, that marks the onset of the 3D isotropic Heisenberg (IH) behavior, shift to lower temperatures. For a given t, the width of ACR as well as the characteristic temperatures Tdip and TIH∗ increase with decreasing (increasing) Fe (Cr) concentration. Consistent with these observations, the ratios involving nonlinear ac magnetic susceptibilities obey the generalized magnetic equation of state with 3D ID critical exponents and the value of Tc same as that determined from χ1(T). A quantitative comparison between theory and experiment highlights certain limitations of the existing theories. The films with t≲20nm do not exhibit 3D IH-to-3D ID crossover. Instead, the critical behavior of Cr70Fe30 thin films with t=21nm and t=11nm is that of a 3D IH and 3D Ising ferromagnet, respectively. By contrast, a 3D Ising (spin glass) critical behavior is observed in the Cr75Fe25 thin film with t=19nm (t=12nm). Curie temperature, Tc, decreases with film thickness in accordance with the finite-size scaling.

Quantum coherence and quantum phase transition in the XY model with staggered Dzyaloshinsky-Moriya interaction

We investigate the properties of geometric quantum coherence in the XY spin-1/2 chain with staggered Dzyaloshinsky-Moriya interaction via the quantum renormalization-group approach. It is shown that the geometric quantum coherence and its coherence susceptibility are effective to detect the quantum phase transition. In the thermodynamic limit, the geometric quantum coherence exhibits a sudden jump. The coherence susceptibilities versus the anisotropy parameter and the Dzyaloshinsky-Moriya interaction are infinite and vanishing, respectively, illustrating the distinct roles of the anisotropy parameter and the Dzyaloshinsky-Moriya interaction in quantum phase transition. Moreover, we also explore the finite-size scaling behaviors of the coherence susceptibilities. For a finite-size chain, the coherence susceptibility versus the phase-transition parameter is always maximal at the critical point, indicating the dramatic quantum fluctuation. Besides, we show that the correlation length can be revealed by the scaling exponent for the coherence susceptibility versus the Dzyaloshinsky-Moriya interaction.