Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate correlations parallel to the layering in the diagonally layered model with periodv=2, the so-called “general square lattice” model (GS). If the model has a finite critical temperature,T _c>0, we have a spontaneous magnetization belowT _c vanishing atT _c with the Ising exponent β=1/8. AtT _c correlations decay algebraically with critical exponnet η=1/4 and exponentially forT>T _c. In the frustrated case we have oscillatory behaviour superposed on the exponential decay where the wavevector of the oscillations changes at some “disorder temperature”T _D(>T _c) from commensurate to temperature-dependent in commensurate periods. If the critical temperature vanishes,T _c=0 we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index η=1/2, i.e.T=0 is thus a critical point.     

Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in horizontal direction. We calculate correlations parallel to the layering in the horizontally layered model with periodv=2. If the model has a finite critical temperature,T _c>0, the order parameter in the frustrated case may become discontinuous forT0. Correlations atT=T _c decay algebraically with critical exponent =1/4 and exponentially forT>T _c. If the critical temperature vanishes,T _c=0, we always have exponential decay at finite temperatures, while atT=T _c=0 we encounter either long-range order or algebraic decay with critical index =1/2, i.e.T=0 is thus a critical point.Work performed within the research program of the Sonder forschungsbereich 125 Aachen-Jülich-Köln     

Phase transitions of “extended” Ising models on a square lattice

The ferromagnetic square lattice Ising spin system is dynamically coupled to another set of Potts variables . We show that the usual Ising phase transition is universally preserved, but the transition temperatureT _c is shifted upwards. To investigate the transition and to calculateTM _c we use both a method by Müller-Hartmann-Zittartz as well as a systematic expansion about the soluble Ising limit. The comparison shows that the MHZ-formula forT _c is presumably a very accurate fit to the correct transition temperature. The results are relevant for special cases of more generalq-state models, for instance the Ashkin-Teller model.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Extremity of the disordered phase in the Ising model on the Bethe lattice

We prove that the disordered Gibbs distribution in the ferromagnetic Ising model on the Bethe lattice is extreme forTT _c ^SG , whereT _c ^SG is the critical temperature of the spin glass model on the Bethe lattice, and it is not extreme forT _c ^SG .     

Frustrated percolation,spin glasses and glasses

Summary The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, exhibits two transitions: a percolation transition at a temperatureT _p with critical exponents of the ferromagnetic (s=1/2)-state Potts model, and a second transition at a lower temperatureT _g in the same universality class of the Ising spin glass model. AboveT _p the time-dependent autocorrelation function is characterized by a single exponential, while forT _p>T>T _g preliminary numerical results show a broad shoulder or plateau typical of a structural glass transition. BelowT _g the system is in glassy state with an infinitely long relaxation time. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Correlations in inhomogeneous Ising models

We study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings are allowed to be of arbitrary strength and sign such that the coupling distribution is translationally invariant either in horizontal or in diagonal direction, i.e. the models have a layered structure. By using transfer matrix techniques the spin-spin correlations are calculated parallel to the layering and are expressed as Toeplitz determinants. After working out the general methods we discuss two special examples in detail: the fully frustrated square lattice (FFS) and the chessboard model, both having no phase transition. At zero temperature correlations in the chessboard model decay exponentially, while in the FFS model one has algebraic decay with a critical index =1/2, i.e.T=0 is a critical point. At finite temperature we find exponential decay in both models with a correlation length determined by the excitation gap in the fermion spectrum. Due to frustration correlations may develop on oscillatory structure and spins separated by an odd diagonal distance are totally uncorrelated at all temperatures.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köla     

Random layered frustration models

We study inhomogeneous two-dimensional Ising models with a random distribution of ferro- and antiferromagnetic couplings,K _ij =±K, or equivalently a random distribution of frustrations. In particular, we considerRandom Layered Frustration models (RLF) where randomness is confined to the vertical direction. These RLF-models are solved exactly, i.e., partition function and free energy are obtained in closed form for an arbitrary random distribution of finite period. The phase transition is of Ising type. A simple formula for the transition temperature is derived which depends only on the mean coupling , but not on other details of the distribution. Both cases,T _c =0 andT _c 0, are possible. Groundstate energy and groundstate degeneracy, or equivalently the rest entropy, are determined. It is found that both the occurence or absence of a phase transition may be accompanied with vanishing or nonvanishing rest entropy. We also show that for the RLF-models a phase transition is excluded when all groundstates are connected with one another by local transformations which presumably holds generally. A remarkable result is that the transition of the ferromagnetic Ising model can be destroyed completely if one replaces an arbitrarily small fraction of ferromagnetic couplings by antiferromagnetic ones in a suitable way.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

μSR investigation of the magnetic ordering in EuAs3

We have investigated the magnetic ordering and the incommensurate-commensurate phase transition in EuAs₃ by zero-field (ZF) and longitudinal-field μSR. In the commensurate phase, stable at temperatures below T_L=10.3 K, the ZF muon signal exhibits oscillations corresponding to four muon precession frequencies the lowest of which behaves anomalously. The muon signal shows no oscillation but exponential decay in the incommensurate phase stable in temperature range from T_L≈10.3 K up to T_N≈11 K. The temperature dependence of the fitted relaxation rate shows divergence-like behaviour at the ordering temperature T_N≈11 K and also at the lock-in transition T_L≈10.3 K. The results are in qualitative agreement with those previously obtained by neutron and X-ray magnetic scattering investigations except for the anomalous temperature dependence of the lowest frequency in the commensurate phase. We propose a model for this anomalous behaviour.     

Layered Ising models on triangular and honeycomb lattices

We study inhomogeneous Ising models on triangular and honeycomb lattices. The nearest neighbour couplings can have arbitrary strength and sign such that the coupling distribution is translationally invariant in the direction of one lattice axis, i.e. the models have a layered structure. By using a transfer matrix method we derive closed form expressions for the partition functions and free energies. The critical temperatures are calculated. Phase transitions at a finite critical temperature are universally of Ising type. Models with no phase transition may show different behaviour atT=0, which is explicitly shown for fully frustrated models on square, triangular and honeycomb lattices. Finally, generalizations to layered Ising models on more general lattices are discussed.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

On the purity of the limiting gibbs state for the Ising model on the Bethe lattice

We give a proof that for the Ising model on the Bethe lattice, the limiting Gibbs state with zero effective field (disordered state) persists to be pure for temperature below the ferromagnetic critical temperatureT _c ^F until the critical temperatureT _c ^SG of the corresponding spin-glass model. This new proof revises the one proposed earlier.     

Glassy phase and thermodynamics for random field Ising model on spherical lattice in magnetic field

Phase diagram and thermodynamic parameters of the random field Ising model (RFIM) on spherical lattice are studied by using mean field theory. This lattice is placed in an external magnetic field (B). The random field (hi) is assumed to be Gaussian distributed with zero mean and a variance     

Enhanced temperature-independent magnetoresistance below the metal-insulator transition temperature of epitaxial La0.2Nd0.4Ca0.4MnO3 thin films

Epitaxial La_0.2Nd_0.4Ca_0.4MnO₃ thin films have been deposited at 800°C on LaAlO₃ substrate using pulsed laser deposition technique. The structural and magnetotransport properties of the films have been studied. The sharp peak in the temperature dependence of the resistance corresponding to metal-to-insulator transition (T _p) has been observed at a temperature of T _p=82 K, 97 K and 110 K for 0 Oe, 20 kOe and 40 kOe magnetic fields, respectively. The film exhibits a large nearly temperature-independent magnetoresistance around 99% in the temperature regime below T _p. The zero field-cooled (ZFC) and field-cooled (FC) magnetization data at 50 Oe shows irreversibility between the ZFC and FC close to the ferromagnetic transition temperature T _c=250 K. The ZFC temperature data of the film displays ferromagnetic behavior for higher temperature regime T _c=250 K>T>T _p=82 K, and a decrease in magnetization with decreasing temperature up to 5 K below 82 K exhibiting a sort of antiferromagnetic behavior in the low temperature regime (T<82 K=T _p=T _N).     

Monte Carlo study of the Quartet Ising model consistent with selfduality

The transition temperature obtained from recent Monte Carlo calculations for the Quartet Ising model on the fcc lattice deviated by 17% from the exact transition temperatureT _c ^SD required by selfduality which we have proven afterwards. Here we use Monte Carlo results of the internal energy, which agree well with low- and high temperature series, to determine entropy and free energy and obtain aT _c in excellent agreement (±0.1%) with the exact value. The Quartet model on the hcp lattice is shown to be selfdual too; the rapidly converging series for the fcc and the hcp lattice differ only in higher order.Guest stay     

Low-temperature structural phase transition in a monoclinic KDy(WO4)2 crystal

The low-temperature thermal and magnetic-resonance properties of a monoclinic KDy(WO₄)₂ single crystal are investigated. It is established that a structural phase transition takes place at T _c=6.38 K. The field dependence of the critical temperature is determined for a magnetic field oriented along the crystallographic a and c axes. The initial part of the H-T phase diagram is plotted for H∥a. The prominent features of the structural phase transition are typical of a second-order Jahn-Teller transition, which is not accompanied by any change in the symmetry of the crystal lattice in the low-temperature phase. The behavior of C(T) in a magnetic field shows that the transition goes to an antiferrodistortion phase. An anomalous increase in the relaxation time (by almost an order of magnitude) following a thermal pulse is observed at T>T _c(H), owing to the structural instability of the lattice. A theoretical model is proposed for the structural phase transition in a magnetic field, and the magnetic-field dependence of T _c is investigated for various directions of the field. Fiz. Tverd. Tela (St. Petersburg) 40, 750–758 (April 1998)     

Scaling properties of hadron production in the Ising model for quark-hadron phase transition

Earlier study of quark-hadron phase transition in the Ginzberg-Landau theory is reexamined in the Ising model, so that spatial fluctuations during the transition can be taken into account. Although the dimension of the physical system is 2, as will be argued, bothd=2 andd=4 Ising systems are studied, the latter being theoretically closer to the Ginzberg-Landau theory. The normalized factorial momentsF _q are used to quantify multiplicity fluctuations, and the scaling exponentν is used to characterize the scaling properties. It is found by simulation on the Ising lattice thatν becomes a function of the temperatureT nearT _c . The average value ofν over a range ofT<T _c agrees with the value of 1.3 derived analytically from the Ginzberg-Landau theory. Thus the implications of the mean-field theory are not invalidated by either the introduction of spatial fluctuations or the restriction to a 2D system.     

Temperature dependence of the gap in the density of states near the Fermi level in a hole doped manganite

In this paper, we report a model-based quantitative analysis of temperature dependent scanning tunneling spectroscopy (STS) data taken on epitaxial thin films of the hole doped manganite La_0.7Ca_0.3MnO₃. The film, grown on lattice matched NdGaO₃ substrate, has a ferromagnetic transition temperature T_c=268 K. The analysis allows us to evaluate how the tunneling curve evolves across the transition temperature. We find that there is a gap Δ in the density of states (DOS), which peaks at T≈T_c. The gap closes in the ferromagnetic state following the evolution of the magnetization. The gap closing is gradual and not sudden at T=T_c. Above T_c the gap reduces from the peak value and reaches a limiting value of ≈75 meV for T/T_c≥1.1 which is close to the value of 60 meV seen from transport experiments.     

The influence of fixed spins on the thermodynamic behavior of an Ising ferromagnet

We study the thermodynamic behavior of a ferromagnetic Ising system on a Bethe lattice in the presence of given boundary conditions. More specifically, we study the interface of the system when the spins on half of the surface are fixed opposite to the spins on the other half. We find an interface width that remains finite in the whole range (0,T _c ), a feature due to the special topology of the Bethe lattice. We also study the case where the spin on a certain lattice site belonging to a domain is fixed in a direction opposite to the domain magnetization at all temperaturesT _c . We obtain the influence of that spin on the local magnetization, and we find that the fixed spin nucleates a local domain that extends over a distance of only a few lattice sites from it at all temperaturesT _c .     

Oxygen-vacancy ordering in the YBa2Cu3Oz basal plane studied by the cluster variation method

The cluster variation method is used to calculate a phase diagram for a two-dimensional Ising model representing the Cu₂O plane of the high-T _c superconductor YBa₂Cu₃O_z. Both first (V ₁ and second-neighbor (V ₂) interactions are considered, withV ₂/V ₁= –1/2; At high temperatures, the transition from the disordered (tetragonal) to the ordered (orthorhombic) phase is second-order. A tricritical point is found below which phase separation occurs. Fractional site occupancy and second-neighbor pair correlations are calculated as a function of temperature. The relevance of the model to the thermodynamics of ordering in the high-T _c compound is discussed.     

The low-temperature properties of the one-dimensional fluid

The low-temperature properties of a one-dimensional fluid with hard core attractive nearest-neighbor interactions have been investigated. The fluid exhibits a critical behavior nearT=0 which is, in some respects, analogous to that of the one-dimensional Ising models. With the proper choice of scaling variables the singular part of the appropriate thermodynamic potential has the same homogeneous scaling form as the Ising model. The correlations in the scaling region have a more complex structure than in the Ising model but do have a long-ranged part of scaling form. TheT=0 limit in the scaling region gives states of low density and zero pressure whose correlations are those of a two-phase state, of which one component is a perfect crystal phase and the other is a zero density phase. The positive pressureT=0 states are single-phase perfect crystal states whose long-range order develops continuously asT approaches zero. Those Fourier components of the correlations, which correspond to reciprocal lattice vectors, diverge asT approaches zero; hence, the transition is second-order, unlike higher-dimensional systems.     

Ising-type critical exponents of the fully frustrated spin-1/2 Heisenberg FM/AF square bilayer at a critical magnetic field

The fully frustrated spin-1/2 Heisenberg FM/AF square bilayer in a magnetic field with the ferromagnetic inter-dimer interaction and the antiferromagnetic intra-dimer interaction is explored by the use of localized many-magnon approach, which allows to connect the original purely quantum Heisenberg spin model on a square bilayer with the effective ferromagnetic Ising model on a simple square lattice. Magnetization and specific heat are investigated exactly at a field-driven phase transition from the singlet-dimer phase towards the fully saturated ferromagnetic phase, which changes from a discontinuous phase transition to a continuous one at a certain critical temperature. The mapping correspondence between the spin-1/2 Heisenberg FM/AF square bilayer and the ferromagnetic Ising square lattice suggests for this special critical point of the spin-1/2 Heisenberg FM/AF square bilayer critical exponents from the standard two-dimensional Ising universality class.