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  • 1
    Electronic Resource
    Electronic Resource
    Phase diagrams and magnetic properties of diluted Ising and Heisenberg magnets with competing interactions (1979)
    Springer
    The European physical journal 36 (1979), S. 161-177 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Ising and Heisenberg magnets with nearest-neighbor ferromagnetic exchangeJ 1 and next-nearest antiferromagnetic exchangeJ 2 and randomly distributed frozen-in nonmagnetic impurities of arbitrary concentration 1−x are studied by several methods: systematic series expansions inx, 1−x and inverse temperature (1/T) as well as Monte Carlo simulation. Depending onR≡J 2/J 1,T andx the model is in paramagnetic, ferromagnetic, antiferromagnetic or spin glass phases. The microscopic magnetic structures of all these phases are investigated and found to be more complicated than usually (e.g., the ferromagnetic state contains spins and clusters either aligned antiparallel or not aligned at all, when “frustration” effects make bonds ineffective). We suggest that the concentrationx c of magnetic ions below which no (anti-)ferromagnetic long range order occurs depends onR continuously, andx c →1 at the multicritical point (R m ,T=0) where the order changes from ferromagnetic to antiferromagnetic. Our results for phase diagram, susceptibility etc. are compared to recent data on the Eu x Sr1−x S system and very good agreement is found.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01320217
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  • 2
    Electronic Resource
    Electronic Resource
    Behavior of the electrical resistivity at phase transitions in binary alloys (1976)
    Springer
    The European physical journal 24 (1976), S. 407-415 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The excess resistivityΔ ρ of binary alloys is calculated in the Born approximation for the scattering of quasifree electrons from the atomic disorder.Δ ρ can be represented as the convolution of the structure functionS(q) and the fourier transform of the effective potential. The critical anomaly ofΔ ρ is derived from scaling expressions forS(q), both for alloys which undergo unmixing and for order-disorder transitions. The variation ofΔ ρ with concentration and temperature in the vicinity of a critical point is obtained. The time-dependence of the resistivity of alloys after a sudden quench into the two-phase region is also calculated, using computer simulation data forS(q,t), and a maximum ofΔ ρ is found for zones with linear dimension of 8–12 lattice spacings. All these results are in fair agreement with the available experiments. As a further possible application, we obtain the critical exponent for the nonlinear relaxation of the resistivity of an alloy close to the order-disorder transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01351533
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  • 3
    Electronic Resource
    Electronic Resource
    On the theory of spinodal decomposition in solid and liquid binary mixtures (1978)
    Springer
    The European physical journal 30 (1978), S. 183-195 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The kinetics of phase separation is discussed with emphasis on the transition between spinodal decomposition and nucleation. A reanalysis of the theory of Langer, Baron and Miller shows that it exhibits a spinodal line somewhat closer to the coexistence curve than the meanfield spinodal. There the same (as we think unphysical) critical singularities occur as in Cahn-Hilliard theory. The precise location of this spinodal line depends on the cell size of the coarse graining. For concentrations less than the spinodal one the structure factorS(k, t) converges then towards the structure factor of the metastable onephase state, implying an infinite lifetime of the latter. In order to include the effects of nucleation and growth we hence present an alternative treatment, extending our previous work on cluster dynamics. From a simple approximation for the radial concentration distribution function of clustersS(k, t) is computed numerically. Even at rather low concentrations the time evolution ofS(k, t) is then similar to what Langer et al. find at high concentrations, implying a very gradual transition from nucleation and growth to spinodal decomposition, at least for parameter values appropriate to the Ising model. This treatment, which is consistent with Lifshitz-Slyozov's coarsening law at late times, is extended to the early stages of phase separation in liquid mixtures.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01320985
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  • 4
    Electronic Resource
    Electronic Resource
    On the nature of the ordering in Ising spin glasses (1978)
    Springer
    The European physical journal 30 (1978), S. 313-324 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Monte Carlo studies of the Ising square lattice and simple cubic lattice with a random (symmetric Gaussian) nearest-neighbor exchange are extended, with emphasis on the behavior at zero temperature and at very long “observation” times. Characterizing a ground-state spin configuration by a vector we found that projections of two ground states on each other are typically of order zero. We observe that the order parameterΨ decreases under the action of a homogeneous magnetic field and vanishes at a critical field. The zero-field susceptibility at zero temperature is found to be finite for both two and three dimensions. The anomalous slow relaxation observed in simulations of spin glasses is traced back to the high ground-state degeneracy. Two sources of anomalous relaxation are identified: (i) disappearance of large domains with (on the average) wrong orientation of the order parameter; and (ii) diffusion of order parameter orientation in a finite system with continuous symmetry of the order parameter. Case (i) is exemplified by computations on a two-dimensional Mattis spin glass model. We find that the observations of Bray and More cannot be maintained asfirm evidence against a phase transition, althoughfirm evidence in favor of a transition is also lacking. With the hypothesis that a transition occurs, a cluster description is used to derive some relations characterizing its singularities. Our Monte Carlo simulations give the field-dependence of the Edwards-Anderson order parameterq atT f and give Chalupa's exponentδ q as about 5 in two dimensions. Our scaling theory shows that a spin-glass transition may occur with finite susceptibilityχ q , which offers a possible interpretation of the series-expansion results of Fisch and Harris.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01320037
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  • 5
    Electronic Resource
    Electronic Resource
    Comparative monte Carlo study of ising spin glasses in two to five dimensions (1979)
    Springer
    The European physical journal 34 (1979), S. 97-105 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Monte Carlo simulations of the Edwards-Anderson-Ising spin glass with Gaussian distribution of nearest-neighbor exchange forces in four and five dimensions are performed to check the speculation thatd=4 is the lower critical dimensionality. In contrast to this expectation we find no qualitative difference at all to the results in two and three dimensions. We still find that on not too long time-scales there is an apparently rather well defined freezing temperatureT f , where the susceptibility has a cusp, and belowT f nonzero order parametersq, ψ can be found as ford=2, 3. But even ford=5 the decay of the Edwards-Anderson order parameter belowT f is found to be consistent with a logarithmic variation over several decades of observation time. The possible interpretations of this result are discussed. Our data thus suggest that either there is no equilibrium phase transition in all these dimensions, or more likely that a phase transition exists for 2≦d≦5 but the properties of the ‘ordered phase’ may be rather peculiar.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01362783
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  • 6
    Electronic Resource
    Electronic Resource
    Ordering and phase transitions in ising systems with competing short range and dipolar interactions (1979)
    Springer
    The European physical journal 34 (1979), S. 375-392 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ 2/a 3. ForJa 3/µ 2〈−1.3384 the ground-state is antiferromagnetic, while for −1.3384〈Ja 3/µ 2〈0.1270 the ground state consists of ferromagnetic rows (in spin direction) arranged antiferromagnetically in the plane perpendicular to it. AtJa 3/µ 2=0.1279 the structure changes to a layered antiferromagnetic structure with a twocomponent order parameter, while forJa 3/µ 2〉0.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa 3/µ 2 where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero. The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa 3/µ 2 of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01325203
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  • 7
    Electronic Resource
    Electronic Resource
    Effective field distribution and time-dependent order parameters of ising and heisenberg spin glasses (1977)
    Springer
    The European physical journal 26 (1977), S. 339-349 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Spin Glasses are represented as assemblies of magnetic clusters interacting with random forces. It is shown that this model reduces to the Edwards-Anderson model by suitable scaling transformations of the variables, and that thereby several discrepancies between theory and experiment are eliminated. Then new computer simulation results are presented and analyzed. It is shown that the distribution of effective fields behaves asP(H eff)∝H eff 2 (Heisenberg) orP(H eff)∝ const (Ising) for smallH eff, while it is a gaussian for largeH eff. In contrast to mean-field treatments of Klein, the width of this distribution has no drastic dependence on temperature. We then show that the Edwards-Anderson order parameter relaxes asq(t)∝τ A /t at high enough temperatures, while our recently introduced order parameterΨ(t)∝exp(−t/τ). Bothτ A ,τ and the susceptibilityχ Ψ seem to diverge at the freezing temperature, and the associated exponents are estimated. The smooth behavior of the specific heat is interpreted in terms of an exponentα 〈 −1. While our description is qualitatively similar to the cluster percolation model of Smith, it is shown that the actualΨ-cluster distribution is not that of a percolation problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01570744
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  • 8
    Electronic Resource
    Electronic Resource
    Linear and nonlinear relaxation and cluster dynamics near critical points (1976)
    Springer
    Journal of statistical physics 15 (1976), S. 267-297 
    Details
    ISSN: 1572-9613
    Keywords: Critical points ; relaxation ; clusters ; cluster waves ; linear response ; nonlinear response ; Ising models ; Glauber models ; lattice dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The critical slowing down of anisotropic magnets, binary mixtures, and systems undergoing structural transitions is interpreted in terms of suitable defined “clusters,” their growth, and their motions (cluster reactions, cluster diffusion, and cluster waves). Our previous studies of the Glauber model are extended considerably by numerical calculations, including the use of the cluster model of Reatto and Rastelli. The behavior of the relaxation function is very insensitive to the details of the models used. A scaling theory of nonlinear response is given, which is far more general than the cluster dynamics treatment. Two different cases occur:(i) at fixed “relative nonlinearity” the critical exponents agree with the corresponding exponents of linear response; (ii) if the initial state is held fixed, different exponents are found, however, which agree with predictions of Racz, and are consistent with Monte Carlo simulations of the nonlinear slowing down of the energy in kinetic Ising models.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01023054
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  • 9
    Electronic Resource
    Electronic Resource
    Nonlinear relaxation at first-order phase transitions: A Ginzburg-Landau theory including fluctuations (1979)
    Springer
    The European physical journal 32 (1979), S. 195-213 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Kinetics of phase transitions are investigated in systems with nonconserved one-component order parameter (i.e., generalized time-dependent Ginzburg-Landau models ind dimensions). The correct static critical behavior as well as fluctuation effects on the kinetics are incorporated by a suitable adaptation of the theory on spinodal decomposition by Langer, Baron and Miller. Both the case of quenches from temperaturesT above to below the critical pointT c and the case of magnetic field changesΔH from positive to negative values are treated, and both time-dependent order parameter 〈m(τ)〉 and structure factorS(q, τ) are obtained numerically ford=2, 3. In the case of quenches atH=0, we find that 〈m(τ)〉≡0 andS(q, τ) —S(q, ∞)∝ exp(−τ 1/2/7.2) $$\tilde S(q\tau ^{ - 1/2} )$$ , withS(q, ∞)∝q −2. In the case of field changes we find that forH not exceeding some critical valueH * the system is trapped in a metastable state with infinite lifetime. In contrast to the meanfield-spinodal, the susceptibility does not seem to diverge atH *. These results are compared with other treatments, in particular the Monte Carlo simulations of kinetic Ising models by Binder and Müller-Krumbhaar. While our theory describes some properties of the metastable states reasonably,H * distinctly exceeds the observed limit of metastability. We argue that the present theory does not take into account nucleation fluctuations, and also fails to describe correctly the domain growth in the late stages of the relaxation. Contrary to Langer et al. we suggest that “universality” holds for nonlinear relaxation and spinodal decomposition nearT c .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01320116
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  • 10
    Electronic Resource
    Electronic Resource
    Dynamics of the generalized Glauber-Ising chain in a magnetic field (1978)
    Springer
    Journal of statistical physics 18 (1978), S. 423-444 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; master equation ; clusters ; nonlinear response ; relaxation functions ; biopolymers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A one-dimensional kinetic Ising model with nearest neighbor interactionJ and magnetic fieldH ⩾ 0 is treated in both linear and nonlinear response, using the most general single spin-flip transition probabilities that depend on nearest neighbor states only. The dynamics is reformulated in terms of kinetic equations for the concentration nl +(t) [@#@ nl(t) of clusters containingl up- [or down-] spins, which is exact in the homogeneous case. The initial relaxation time τ* of the magnetization is obtained rigorously for arbitraryJ, H, and temperatureT. The relaxation function is found by numerical integration forJ/T 〈 2. It is shown that “coagulation” of minus-clusters becomes negligible for bothJ/T andH/T large, and the resulting set of equations is solved exactly in terms of an eigenvalue problem. A perturbation theory is developed to take into account the neglected coagulation terms. The relaxation function is found to be non-Lorentzian in general, in contrast to the Glauber results atH = 0, which are recovered as a special case. In addition, nonlinear and linear relaxation functions differ forH ≠ 0. Consequences for the application to biopolymers are briefly mentioned.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014516
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