Three-dimensional Spin System Research Articles

Nonequilibrium dynamical phase transition of 3D kinetic Ising/Heisenberg spin system

We have studied the nonequilibrium dynamic phase transitions of both three-dimensional (3D) kinetic Ising and Heisenberg spin systems in the presence of a perturbative magnetic field by Monte Carlo simulation. The feature of the phase transition is characterized by studying the distribution of the dynamical order parameter. In the case of anisotropic Ising spin system (ISS), the dynamic transition is discontinuous and continuous under low and high temperatures respectively, which indicates the existence of a tri-critical point (TCP) on the phase \linebreak boundary separating low-temperature order phase and high-temperature disorder phase. The TCP shifts towards the higher temperature region with the decrease of frequency, i.e. TTCP=1.33×exp(−ω/30.7). In the case of the isotropic Heisenberg spin system (HSS), however, the situation on dynamic phase transition of HSS is quite different from that of ISS in that no stable dynamical phase transition was observed in kinetic HSS after a threshold time. The evolution of magnetization in the HSS driven by a symmetrical external field after a certain duration always tends asymptotically to a disorder state no matter what an initial state the system starts with. The threshold time τ depends upon the amplitude H0, reduced temperature T/TC and the frequency ω as τ = C.ωα.H0−β.(T/TC)−γ.

Spin dynamics in the BEC phase of the S=1/2 quantum spin system TlCuCl 3

The copper salt S=1/2 TlCuCl 3 is a three-dimensional quantum spin system with a singlet ground-state of dimer origin. A spin energy gap Δ≈0.7 meV separates the ground-state from the triplet waves, which propagate along all directions in reciprocal space. Across the quantum critical point at H c= Δ/ gμ B Bose–Einstein condensation of the triplet quasi-particles has been observed. The inelastic neutron scattering spectra at H> H c proof the coexistence of a gapless Goldstone mode, which has a linear dispersion, with renormalized quadratic Zeeman modes.

Unconventional critical behavior of magnetic susceptibility as a consequence of phase separation and cluster formation in La0.7Ca0.3MnO3 thin films

Nonuniversal critical behavior of the dc magnetic susceptibility χ−1(T)−χ−1(TC)∼(T/TC−1)γ≡τγ is observed near the paramagnetic (PM) to ferromagnetic (FM) transition in La0.7Ca0.3MnO3 film samples. The value of γ≈1.4 obtained for 0<τ<τ1 with τ1≈0.05–0.09 corresponds to a three-dimensional Heisenberg spin system and that of γ≈2.4 for τ1<τ<τ2 with τ2≈0.2–0.3 to a two-dimensional percolation system. This behavior is attributed to phase separation by presence of FM clusters with temperature dependent correlation length in the PM matrix of the film.

THREE-DIMENSIONAL GONIHEDRIC SPIN SYSTEM

We perform Monte–Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature – gonihedric action. We study the anisotropic model when the coupling constants βS for the space-like plaquettes and βT for the transverse-like plaquettes are different. In the two limits βS = 0 and βT = 0 the system has been solved exactly and the main interest is to see what happens when we move away from these points towards the isotropic point, where we recover the original model. We find that the phase transition is of first order for βT = βS ≈ 0.25, while away from this point it becomes weaker and eventually turns to a crossover. The conclusion which can be drawn from this result is that the exact solution at the point βS = 0 in terms of 2D-Ising model should be considered as a good zero-order approximation in the description of the system also at the isotropic point βS = βT and clearly confirms the earlier findings that at the isotropic point the original model shows a first-order phase transition.

Quantum phase transitions for the three-dimensional orthogonal-dimer spin system

We discuss the phase diagram of the three-dimensional orthogonal-dimer system for the compound SrCu 2(BO 3) 2. By performing the computer-aided series expansion, we investigate quantum phase transitions among the dimer phase, the frustration-induced disordered phase and the magnetically ordered phase. It is claimed that the compound SrCu 2(BO 3) 2 is located in the dimer phase close to a tri-critical phase transition point.

Magnetic interaction in low density carrier ferromagnetic semiconductors

We developed a Monte Carlo method to study the magnetic and transport properties of low density carrier ferromagnetic semiconductors. The magnetization of local spins is calculated for the two- and the three-dimensional Ising spin systems interacting with the electrons. The AC conductivity is also calculated. When the temperature increases from T=0, the spontaneous magnetization of the local spins decreases appreciably even in the low temperature range, and rapidly at the Curie temperature. The intensity of AC conductivity transfers from ω∼0 range to the frequency range characterized by the excitation energy of the magnetic polaron state.

Study on the Magnetic and Transport Properties of Low Density Carrier Ferromagnetic Semiconductors

We developed a Monte Carlo method to study the magnetic and transport properties of low density carrier ferromagnetic (FM) semiconductors. The calculation is carried out for the two- and three-dimensional Ising spin system interacting with electrons through the s-d exchange coupling. When the temperature increases from T =0, the spontaneous magnetization of the local spins decreases appreciably in the low T range, and steeply at the Curie temperature ( T C ). The initial decrease is caused by the almost complete escape of electrons from the spin flipped sites, and accumulation in the FM region. The electron spin polarization is complete in the whole FM temperature range except very near T C . The Curie temperature shifts to low T side from the value estimated based on the RKKY model as the exchange constant increases. The critical-scattering-like peak of the resistivity appears near T C when the exchange interaction is not so strong, but it disappears when the interaction is strong. In the former cases, t...

Magnetic phase transition in amorphous Cr/TbDyFe thin-film multilayers

The Magnetic phase transition in amorphous thin-film multilayers is investigated, for the first time, by deducing the critical exponents using the conventional techniques to analyze phase transitions, e.g., the Modified Arrott Plots, Kouvel-Fisher Method, Scaling Equation of State Analysis and the critical isotherm at the Curie point. The magnetic phase transition in this material is characterized by the critical exponent values close to those corresponding to the three-dimensional Heisenberg spin system with nearest-neighbor interactions.

Magnetic Phase Transition in Amorphous Cr/TbDyFe Ultrathin Film Multilayers

We have made an attempt to study the second-order magnetic phase transition in Cr/TbDyFe ultrathin film multilayers by characterizing it with the help of critical exponents deduced from magnetization measurements. The thickness of these films falls in the monolayer range and hence each of these films could be approximated to systems with a lattice dimensionality of two. However, we ended up with the critical exponent values close to those for a three-dimensional Heisenberg spin system. The reasons for this could be attributed to the interactions between spins coupled through the interlayer of Cr.

Magnetic phase transition in amorphous Fe 73.5Cu 1Nb 3Si 13.5B 9 alloy

We have obtained the critical exponents, the corresponding amplitudes and the universal amplitude ratios for the amorphous Fe 73.5Cu 1Nb 3Si 13.5B 9 alloy from detailed bulk magnetization measurements performed in the critical region near the magnetic phase transition temperature. The critical exponents determined are β, γ, γ′ and δ, among which β describes the temperature dependence of the spontaneous magnetization, γ ( T ≥ T C) and γ′ ( T ≤ T C) describe the temperature dependence of the zero-field susceptibility, and δ describes the field dependence of the magnetization at the Curie temperature, T C. The values of T C obtained in the present investigation match very well those reported in the literature. The critical exponent values are very close to those theoretically predicted for the three-dimensional Heisenberg spin system.

TWO- AND THREE-DIMENSIONAL SPIN SYSTEMS WITH GONIHEDRIC ACTION

We perform numerical simulations of the three-dimensional spin system with competing interaction that has been proposed in Refs. 1–3 as a model of random surfaces with gonihedric action. For the system with a self-intersection coupling constant k equal to one we observe the second-order phase transition at the temperature βc≃0.44. We suggest the full set of order parameters, which characterize the structure of the vacuum states and of the phase transition.

Searching for spontaneous magnetic order in an organic ferromagnet. μSR studies of β-phase p-NPNN

Zero-field muon spin rotation (ZF-μSR) studies in the recently synthesized organic ferromagnet β-phase p-NPNN are reported. Our measurements, using a microscopic magnetic probe, provide the first direct observation of spontaneous magnetic order in p-NPNN. The behaviour of the system is close to that of an isotropic three-dimensional (3D) Heisenberg spin system.

Solutions of the quantum three-simplex equation without spectral parameters

With the help of computer symbolic manipulation (Mathematica) the spectral parameter free solutions of the quantum three-simplex equation, which is a multidimensional generalization of the Yang-Baxter equation by Frenkel and Moore [Commun. Math. Phys. 138 (1991) 259], have been obtained. These solutions depend on the solutions of the 1 + 1 Yang-Baxter equation and help to understand the underlying algebra that is related to a higher braid group [Yu.I. Manin and V.V. Schechtman, Adv. Stud. Pure Math. 17 (1989) 289], which may have a relation with some special kind of three-dimensional lattice spin systems.

Magnetic phase transitions inCocMg1−cCl2and stage-2CocMg1−cCl2graphite intercalation compounds

Pristine Co c Mg 1-c Cl 2 and stage-2 Co c Mg 1-c Cl 2 graphite intercalation compounds (GICs) (0≤c≤1) approximate site-diluted three-dimensional (3D) and two-dimensional (2D) XY spin systems, respectively. We have studied the magnetic phase transitions of these two systems by using dc and ac magnetic susceptibilities. We find that the reduced critical temperature of stage-2 Co c Mg 1-c Cl 2 GIC is almost the same as that of Co c Mg 1-c Cl 2 for c>0.7. The effect of the dimensionality on the dilution with Mg ions becomes significant below c≃0.7

A new approach to description of phase transitions in spin systems

Spin systems with a long-range sign-alternating interaction undergoing a fluctuation phase transition are investigated. A new approach to the calculation of corresponding thermodynamic quantities is suggested. It is based on the summation of the principal part of high-temperature series in z -1 performed in a way which leads to a correct description of the critical behavior in the one-loop approxiamtion ( z is the number of the neighbor spins interacting with a given one). The accuracy of the method is of a universal nature; for three-dimensional spin systems the error of some particular calculations is below 2%.

Magnetic ordering in the three-dimensional frustrated Heisenberg model.

Monte Carlo simulations of moderately frustrated three-dimensional Heisenberg spin systems show evidence for two distinct ordering events. The upper one, at ${\mathit{T}}_{\mathit{c}}$, marks the onset of long-range ferromagnetic order and exhibits fluctuations which scale as the system size. The lower event, at ${\mathit{T}}_{\mathit{x}\mathit{y}}$, marks the freezing of transverse degrees of freedom and does not affect the long-range order in the system. Critical levels of frustration for the onset of ferromagnetism have been determined on several lattices and a phase diagram is presented.

Properties of the chiral-spin-liquid state.

It is shown that one of the class of variational spin-liquid wave functions recently derived by Wen, Wilczek, and Zee [Phys. Rev. B 39, 11413 (1989)] is identical to the fractional-quantum-Hall analog state proposed by Kalmeyer and Laughlin [Phys. Rev. Lett. 59, 2095 (1987); Phys. Rev. B 39, 11 879 (1989)] and Laughlin [Ann. Phys. (N.Y.) 191, 163 (1989)], and that the neutral spin-1/2 excitations of the two states are also the same. The 1/2 fractional statistics obeyed by these particles is demonstrated explicitly. The spin-spin correlation function and quasiparticle profile for the Wen-Wilczek-Zee states are calculated both numerically and by a hypernetted-chain procedure. Both are consistent with the idea that spontaneous breaking of time-reversal symmetry is an essential feature of any spin state lacking magnetic order. A version of this state for a three-dimensional spin system is reported and shown to have similar properties. A case is made that the neutral spin-1/2 excitations of the three-dimensional spin liquid behave like anisotropic monopoles.

Three-dimensional spin systems without long-range order

Several examples of three-dimensional statistical models with multibody interactions and unusual symmetry properties are studied from a unified point of view. The symmetries of these theories are neither global nor local, but are something in between. In the nomenclature of a recently proposed classification scheme, these theories have a symmetry index, n ⩽ 2, and so have no long-range order when the internal symmetry is continuous. Duality properties and topological excitations of the theories are studied, and their phase diagrams are qualitatively discussed. Similarities between these three-dimensional semi-local theories and ordinary globally-symmetric theories in one and two dimensions are discussed.

Critical exponents by the scaling-field method: The isotropicN-vector model in three dimensions

A numerical technique, termed the scaling-field method, is developed for solving by successive approximation Wilson's exact renormalization-group equation for critical phenomena in three-dimensional spin systems. The approach uses the scaling-field representation of the Wilson equation derived by Riedel, Golner, and Newman. A procedure is proposed for generating in a nonperturbative and unbiased fashion sequences of successively larger truncations to the infinite hierarchy of scaling-field equations. A principle of balance is introduced and used to provide a self-consistency criterion. The approach is then applied to the isotropic $N$-vector model. Truncations to order 13 (10, when $N=1$) scaling-field equations yield the leading critical exponents, $\ensuremath{\nu}$ and $\ensuremath{\eta}$, and several of the correction-to-scaling exponents, ${\ensuremath{\Delta}}_{m}$, to high precision. Results for $N=0, 1, 2, \mathrm{and} 3$ are tabulated. For the Ising case ($N=1$), the estimates $\ensuremath{\nu}=0.626\ifmmode\pm\else\textpm\fi{}0.009$, $\ensuremath{\eta}=0.040\ifmmode\pm\else\textpm\fi{}0.007$, and ${\ensuremath{\Delta}}_{1}\ensuremath{\equiv}{\ensuremath{\Delta}}_{400}=0.54\ifmmode\pm\else\textpm\fi{}0.05$ are in good agreement with recent high-temperature-series results, though exhibiting larger confidence limits at the present level of approximation. For the first time, estimates are obtained for the second and third correction-to-scaling exponents. For example, for the Ising model the second even and first odd correction-to-scaling exponents are ${\ensuremath{\Delta}}_{422}=1.67\ifmmode\pm\else\textpm\fi{}0.11$ and ${\ensuremath{\Delta}}_{500}=1.5\ifmmode\pm\else\textpm\fi{}0.3$, respectively. Extensions necessary to improve the accuracy of the calculation are discussed, while applications of the approach to anisotropic $N$-vector models are described elsewhere. Finally, the scaling-field method is compared with other techniques for the high-precision calculation of critical phenomena in three dimensions, i.e., high-temperature-series, Monte Carlo renormalization-group, and field-theoretic perturbation expansions.

Limitations of spin-wave theory inT=0spin dynamics

The $T=0$ dynamics of a family of one-dimensional quantum spin systems with fully ordered (ferromagnetic or spin-flop) ground states is investigated. By rigorous calculations, it is demonstrated that the $T=0$ dynamic structure factor is, in general, not a $\ensuremath{\delta}$ function as predicted by linear spin-wave theory but characterized by more complicated structures with nonzero linewidths. The exact result approaches the spin-wave result in the classical limit $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The results of this study demonstrate how quantum effects may invalidate spin-wave theory even in the presence of saturated magnetic long-range order. Hence the failure of spin-wave theory is not necessarily linked to the absence or strong reduction of long-range order typical for one-dimensional quantum spin systems. The unreliability of spin-wave theory has therefore to be suspected also for the dynamics of three-dimensional quantum spin systems where the long-range order is always strong at $T=0$.