W. Kinzel

Phase transitions on centred rectangular lattice gases: A model for the adsorption of H on Fe(110)

Abstract A lattice gas model on a centred rectangular lattice with short range pair and triple interactions is investigated. Ground state calculations give a large number of ordered structures. Phase diagrams, correlation functions and critical exponents of several transitions to (2 × 1), (3 × 1) and (4 × 1) structures are obtained from transfer matrix scaling and Monte Carlo methods. Isotropic scaling is verified. Many experimental observations for the adsorption of H on Fe(110) are reproduced by this lattice gas model.

Lattice gas models with competing interactions

Abstract The phase diagrams of lattice gas models on square and centred rectangular lattices with short range competing pair interactions and three-body forces are studied using Monte Carlo techniques and the transfer matrix method. A variety of commensurate (C) phases can be described as observed experimentally for adsorbed monolayers like H on Pd(100), O on W (110) and especially H on Fe(110). In addition, due to the competition between different C phases incommensurate (IC) structures may occur. Their properties and related aspects (C-IC transitions, disorder lines) are discussed in connection with the widely studied ANNNI model, and general concepts on two-dimensional C and IC phases and experiments. Also dynamic properties — such as the self-diffusion of the adsorbate at the surface — are briefly mentioned.

Theoretical aspects of order-disorder transitions in adsorbed layers

Abstract Lattice gas models for the description of registered monolayers adsorbed on surfaces are introduced and theoretical predictions for the phase transitions of these systems are briefly reviewed. It is shown that rather complicated phase diagrams may result from simple model assumptions about adsorbate-adsorbate interactions. These phase diagrams, as well as adsorption isotherms, ordering energies, etc., may be calculated reliably either from Monte Carlo simulation or from real-space renormalization group methods, while mean-field-like approximations often are inadequate. There is particular interest in the critical behavior of the order-disorder transitions of adsorbed layers, since they constitute physical realizations of universality classes such as the three or four-state Potts model, as well as those where nonuniversal critical behavior may occur. Finally a brief comparison to experimental results on the phases of H on Pd(100) and Fe(110) is made.

Phase diagrams and magnetic properties of diluted Ising and Heisenberg magnets with competing interactions

Ising and Heisenberg magnets with nearest-neighbor ferromagnetic exchangeJ1 and next-nearest antiferromagnetic exchangeJ2 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≡J2/J1,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 concentrationxc of magnetic ions below which no (anti-)ferromagnetic long range order occurs depends onR continuously, andxc→1 at the multicritical point (Rm,T=0) where the order changes from ferromagnetic to antiferromagnetic. Our results for phase diagram, susceptibility etc. are compared to recent data on the EuxSr1−xS system and very good agreement is found.

Storing and Retrieving Information in a Layered Spin System

We introduce a neural network model with layered architecture and binary (spin) variables. Hebbian rules are used to define unidirectional couplings between spins of adjacent layers. A fast learning algorithm produces couplings that store a large number of random patterns, and efficiently recognizes noisy patterns. Performance of this network is compared with spin-glass type models of pattern recognition.

Monte Carlo calculations of phase diagrams of Ising systems with competing interactions

Abstract Fcc antiferromagnets with nearest ( J nn ) and next-nearest neighbor exchange ( J nnn ) in a field H are studied by Monte Carlo methods. For J nnn = 0, H = H cl = 4¦J nn ¦ the “fully frustrated” system stays always disordered. In a centered rectangular lattice, layered structures (2×1), (3×1) and an incommensurate phase are found.

Magnetic ordering in diluted Ising and Heisenberg systems with competing interactions: Theory and application to EuxSr1−xS

Abstract We discuss the phase diagram of diluted Ising and Heisenberg systems with ferromagnetic nearest neighbor J1 and antiferromagnetic next nearest-neighbor exchange J2. Depending on J 2 J 1 , temperature and dilution both ferromagnetic, antiferromagnetic, spin-glass and paramagnetic phases occur.

Susceptibility and spin correlations in spin glasses with short - range interactions

Abstract Static and dynamic susceptibilities are discussed for the Ising square lattice with nearest-neighbor gaussian exchange and diluted Heisenberg magnets with exchange between nearest and next-nearest neighbors. The freezing transition is of dynamic nature. Contradictory experimental evidence is explained by effects due to a re-entrant ferromagnetic phase boundary.

The spin glass transition: a comparison of Monte Carlo simulations of nearest-neighbor Ising Edwards-Anderson models with experiments

Numerical studies of Ising square lattices with random bonds (Jij=±J or drawn from a gaussian distribution) are reviewed. Particular attention is paid to the temperature- and field dependence of the equilibrium magnetization M(H,T). While for a symmetric bond distribution the zero-field susceptibility trivially follows a Curies law Xo∝ T−1, the nonlinear susceptibility Xnl shows a dramatic temperature-dependence, which can nearly be mistaken for a power-law divergence at a freezing temperature Tf. These findings are compared in detail with corresponding experimental data, including possible “scaling” representations. We relate this behavior to the onset of long-range Edwards-Anderson order as T→0, as measured by the correlation function gEA(rij)=[ T 2 ]av

Theory of phase transitions in diluted systems with competing interactions

As a simple model of a diluted system with competing interactions, we first consider an Ising spin system on the square lattice with nearest-neighbour interaction J1 positive, next-nearest-neighbour interaction J2 negative, and where a fraction 1 –x of the spins is removed at random. Systematic expansions in x or 1 –x as well as Monte Carlo calculations are used to investigate the ordering of this model system. It is shown that for broad ranges of x and J2/J1 a spin-glass phase occurs, which consists of (anti-) ferromagnetic clusters coupled together by partially „frustrated“ bond, giving rise to a high ground-state degeneracy. Then we briefly discuss various analytical methods which can be used to calculate spin-glass properties, and compare them with our numerical results. Also other related models are mentioned. Finally we discuss to what extent these models can be applied to randomly mixed molecular crystals.