Magnets with random uniaxial anisotropy: Large-N effective potential and infrared properties

We study the magnetic properties of systems with random uniaxial anisotropy using a large-N effective potential approach for d = 4, 3.It is found that the random interactions induce a strong infrared behavior that prevents the existence of a ferromagnetic phase and massless transverse modes.The transverse susceptibility is finite for all values of the temperature and at d = 4 it has an esential singularity in the couplings. We argue that this is indicative of a mechanism of dynamical mass generation due to the infrared instabilities of the theory.For both d = 4, 3 there is a spin-glass low-temperature phase and a paramagnetic high-temperature phase, the susceptibility having a cusp across the transition.We prove that these phases are stable and that the transverse and longitudinal susceptibilities are equal.     

Spin-freezing processes around the tricritical point in Mn1−xTixSb

Transitions related to the spin-glass phase in Mn_1−xTi_xSb are revisited from the nonlinear ac susceptibility. Near the tricritical point (x≈0.8), the transition between ferromagnetic and reentrant spin-glass states is sharp. At x0.8, an anomally is found slightly above the temperature of usual spin-glass freezing.     

Quantum potts gauge-matter systems at finite temperature

A systematic large-N expansion for gauge-matter Potts systems at finite temperature is presented. This allows us to explore the interior of the phase diagrams, taking into account all terms in the hamiltonian. Calculations are carried out in 3 + 1 and 2 + 1 dimensions and the expansion parameter is $\text{1/N}{}^{\mathrm{<mtext>1</mtext><mtext>d</mtext>}}$, where d is the number of space dimensions. For singly charged matter the Higgs-confinement phase is analytically connected to a high-temperature plasma phase. When the matter fields are multiply charged, both Higgs and confinement phases undergo a finite-temperature phase transition. The free charge phase may or may not undergo a phase transition depending on the number of space-time dimensions. Implications for other models, both abelian and non-abelian are discussed. We also comment on applications to quantum spin systems.     

Strong-coupling planar diagrams,random surfaces,and the large-N phase transition in U(N) lattice gauge theories

The strong-coupling expansion of U(N) gauge theory on a D-dimensional lattice is reformulated in the limit N → ∞ through a set of diagrammatic rules directly for the free energy and Wilson loops. The strong-coupling planar diagrams are interpreted as surfaces embedded in the lattice. The large-N phase transition is related to the entropy of these surfaces. It is shown that the strong-coupling phase of the U(∞) gauge theory terminates with a phase transition of Gross-Witten type only in 2 and 3 dimensions. When D⩾4 the large-N singularity takes place in a metastable phase because of an earlier first-order transition to the weak-coupling phase of the theory.     

Nature of the transition between a ferromagnetic metal and a spin-glass insulator in pyrochlore molybdates

The metal-insulator transition has been investigated for pyrochlore molybdates R(2)Mo(2)O(7) with nonmagnetic rare-earth ions R. The dynamical scaling analysis of ac susceptibility reveals that the geometrical frustration causes the atomic spin-glass state. The reentrant spin-glass phase exists below the ferromagnetic transition. The electronic specific heat is enhanced as compared to the band calculation result, perhaps due to the orbital fluctuation in the half-metallic ferromagnetic state. The large specific heat is rather reduced upon the transition, likely because the short-range antiferromagnetic fluctuation shrinks the Fermi surface.     

Spin-glass phase in the ensemble of amphoteric impurities in a semiconductor

The transition to the spin-glass phase at T = 0 has been found for a two-dimensional ensemble of amphoteric impurities with charge transfer. The characteristics of the charge clustering found in specimens at low temperatures have been investigated. The finite size scaling with the critical exponents v = 0.95 ± 0.05, η = 0.75 ± 0.05 has been found for the spin-glass susceptibility _χSG(L,T) and Binder parameter g(L,T).     

The critical exponents of the matrix-valued Gross-Neveu model

We study the large-N limit of the matrix-valued Gross-Neveu model in d > 2 dimensions. The method employed is a combination of the approximate recursion formula of Polyakov and Wilson with the solution to the zero-dimensional large-N counting problem of Makeenko and Zarembo. The model is found to have a phase transition at a finite value for the critical temperature and the critical exponents are approximated by ν = 1/(2(d − 2)) and η = d − 2. We test the validity of the approximation by applying it to the usual vector models where it is found to yield exact results to leading order in 1/N.     

Reentrant phases in the ± J spin glass

We consider an enlarged phase space of the ±J spin glass which includes the dilute Ising model and the frustrated system. The three orthogonal axes in this space are: (i) The fraction of ferro- to antiferro-magnetic bonds, p; (ii) the ratio of the strengths of the antiferro- to ferromagnetic interacions, q; and (iii) the temperature, T. Within this phase space we observe extended regions of the low-temperature spin-glass phase which is characterized by a unique distribution of the local-order parameter. We observe reentrant phase transitions: for fixed p and q with varying T the distribution of the local order parameter shows paramagnetic, ferromagnetic and then spin-glass phases; for fixed p and T and varying q the distribution shows ferromagnetic to paramagnetic and then spin-glass phases.     

On the behavior of static susceptibilities in spin glasses

Linear and nonlinear susceptibilities of spin glasses in thermal equilibrium are qualitatively discussed in terms of magnetic short-range order. The apparent discrepancy between theoretical results, implying lack of Edwards-Anderson order and hence a divergence of the susceptibility at zero temperature, and experiments showing a susceptibility saturating at finite values, is considered. It is suggested that the susceptibility must indeed have a static maximum if the system exhibits a (frustrated) ferromagnetic phase with a reentrant phase boundary. At the reentrancy point, some exponents of the ferromagnet take twice their normal value, and hence a crossover near this point occurs similar to multicritical points. These observations are used to interpret a number of recent experiments, and it is shown that neither of them proves the existence of a static spin glass phase. As a quantitative example of gradual onset of order without a phase transition in three-dimensional systems, numerical results for susceptibility and specific heat of the fully frustrated Ising fcc antiferromagnet at its critical field are given.Finally the possible coexistence of spin-glass behavior and ferromagnetic long-range order in vector spin glasses with short-range interactions is discussed. Speculative arguments suggest that even for time-scales for which the spins are frozen such a coexistence should not occur, if interactions off-diagonal in the spin components (such as of dipolar origin) are included.     

The magnetic susceptibility of two-dimensional Ising model on a finite-size lattice

The form factor representation of the correlation function of the 2D Ising model on a cylinder is generalized to the case of arbitrary arrangement of correlating spins. The magnetic susceptibility on a lattice, one of whose dimensions (N) is finite, is calculated in both the ferromagnetic and the paramagnetic region of the parameters of the model. The structure of singularities of susceptibility in the complex temperature plane at finite values of N and the transition to the thermodynamic limit N→∞ are discussed.     

The magnetic and superconducting phase diagram of Gd-doped lanthanumsulfides

The system La_3-x( )_xS₄ [where ( ) denotes a vacancy] containing up to 25 at.% Gd is shown to be a model system in which magnetic interactions in metals can be studied. By measuring the temperature dependence of the low field a.c. susceptibility, the superconducting, spin-glass and ferromagnetic transitions can be determined as a function of the Gd concentration. The depression of the superconducting transition temperature mainly follows the theory of Abrikosov and Gor'kov, with a possibility for coexistence of superconductivity and spin-glass magnetic order near a critical concentration of 3 at.% Gd. The transition from spin-glass to ferromagnet is well-defined with the percolation limit for the long range ferromagnetic order at 14 at.% Gd.     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

Effect of the metal-insulator transition on the spin-glass interaction

The effect of the metal-insulator transition on the spin-glass interaction was studied by measuring the magnetic properties of (MnSi)O_X as a function of oxygen content X. As X varies from 0 to 3.6 one changes from a metallic to an insulating spin-glass. The transition at X ≲ 1 is marked by a sharp decrease in the susceptibility and a change of the Curie-Weiss temperature (θ) from ferromagnetic to antiferromagnetic.     

Optimization of Pr(0.9)Ca(0.1)MnO(3) thin films and observation of coexisting spin-glass and ferromagnetic phases at low temperature

Optimization of thin films of small bandwidth manganite, Pr(1-x)Ca(x)MnO3 (for x = 0.1), and their magnetic properties are investigated. Using different pulsed laser deposition (PLD) conditions, several films were deposited from the stoichiometric target material on SrTiO3 (001) substrate and their thorough structural and magnetic characterizations were carried out using x-ray diffraction, atomic force microscopy, x-ray photoelectron spectroscopy (XPS), SQUID magnetometry and ac susceptibility measurements. A systematic investigation shows that irrespective of the growth temperature (between 550 and 750?°C), all the as-deposited films have twin boundaries and magnetic double phases. Post-annealing in partial or full oxygen pressure removes the extra phase and the twin boundaries. Zero-field-cooled magnetization data show an antiferromagnetic to paramagnetic transition at around 100 K whereas the field-cooled magnetization data exhibit a paramagnetic to ferromagnetic transition close to 120 K. However, depending on the oxygen treatments, the saturation magnetization and Curie temperature of the films change significantly. Redistribution of oxygen vacancies due to annealing treatments leading to a change in ratio of Mn3+ and Mn4+ in the films is observed from XPS measurements. Low temperature (below 100 K) dc magnetization of these films shows metamagnetic transition, high coercivity and irreversibility magnetizations, indicating the presence of a spin-glass phase at low temperature. The frequency dependent shift in spin-glass freezing temperature from ac susceptibility measurement confirms the coexistence of spin-glass and ferromagnetic phases in these samples at low temperature.     

The large-N phase transition in the U(N) lattice gauge theory

We present an outline for a proof (the precise details of which will be presented in a follow-up paper) of a large-N phase transition in dimensions greater than two. The critical couplings are calculated in d=3 and d=4 and are found to be β=0.44 and β=0.40, respectively.     

Reentrant spin-glass transition in a dilute magnet

We perform a large-scale Monte Carlo simulation of a dilute classical Heisenberg model with ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions. We found that the model reproduces a reentrant spin-glass transition. That is, as the temperature is decreased, the magnetization increases rapidly below a certain temperature, reaches a maximum value, and then disappears at some lower temperature. The low temperature phase was suggested to be a spin-glass phase that is characterized by ferromagnetic clusters.     

ε-expansion calculations for spin-glasses

The critical properties of the spin-glass transition proposed by Edwards and Anderson are studied using the minimal subtraction method. The universal ratio of the second correction to scaling amplitude to the square of the first for the order parameter susceptibility χ₀ is calculated to first order in ε(ε=6?d). Comparison is made with Fisch and Harris' high temperature series analysis which incorporated Rudnick-Nelson-type corrections to scaling. Within the same formalism the critical exponents are calculated to second order in ε. They agree with the first order ε expansion of Harris, Lubensky and Chen.     

Finite size effects for the dilute coupling Derrida model

There is a certain correspondence between the problems of information theory and spin-glass physics. The Derrida model occupies an important place here, as it is optimal in a certain sense. We have considered finite size corrections in the paramagnetic, spin-glass and ferromagnetic phases. At T = 0 the finite size corrections in the ferromagnetic phase have an important information theoretic meaning. We found singular corrections in the paramagnetic region and finite size corrections in the spin-glass region, which are responsible for the zero-modes. The connection between information theory and spin-glass physics and the physical meaning of finite size corrections are discussed in detail.     

Quantum-mechanically induced asymmetry in the phase diagrams of spin-glass systems

The spin-1/2 quantum Heisenberg spin-glass system is studied in all spatial dimensions d by renormalization-group theory. Strongly asymmetric phase diagrams in temperature and antiferromagnetic bond probability p are obtained in dimensions d>or=3. The asymmetry at high temperatures approaching the pure ferromagnetic and antiferromagnetic systems disappears as d is increased. However, the asymmetry at low but finite temperatures remains in all dimensions, with the antiferromagnetic phase receding from the ferromagnetic phase. A finite-temperature second-order phase boundary directly between the ferromagnetic and antiferromagnetic phases occurs in d>or=6, resulting in a new multicritical point. In d=3, 4, 5, a paramagnetic phase reaching zero temperature intervenes asymmetrically between the ferromagnetic and reentrant antiferromagnetic phases. There is no spin-glass phase in any dimension.     

A Monte Carlo study of the U(2) chiral model

We investigate via the Monte Carlo method the non-linear U(2) matrix sigma model. The average link and specific heat measurements indicate that the apparent phase transition is higher than second order. The U(1) susceptibility and determinantal correlation functions turn out to be order parameters and yield 0.41 as the approximate critical coupling. The role played by topological excitations particularly in the critical region is studied. We also use our work as a stepping stone to obtain a glimpse of the matrix large-N problem. The results all support the conclusions of Green and Samuel. Finally, the implications for gauge theories are discussed.