Intersystem crossing in Fe(II) coordination compounds

Fe(II) spin-crossover systems can be quantitatively converted from the low-spin (LS) to the high-spin (HS) state well below the thermal transition temperature by irradiating either into the metal-ligand charge transfer or d-d absorption bands, and even in low-spin systems a transient population of the HS state can be achieved. This fact can be made use of to determine HS LS relaxation rate constants for a wide variety of Fe(II) spin-crossover and low-spin systems. The HS LS relaxation shows strong deviations from an Arrhenius behaviour, with nearly temperature-independent tunnelling below 70 K and a thermally activated process above 100 K. The range of more than 12 orders of magnitude in the low temperature tunnelling rate constant can be understood in terms of a non-adiabatic multiphonon process, where in the strong vibronic coupling limit an inverse energy gap law holds.     

Solution of the long-range gaussian-random Ising model

The spin glass model of Edwards and Anderson is solved for Ising spins starting from a renormalized diagrammatic expansion. One gets two qualitatively distinct phases for arbitrary external field. The high temperature phase is identical with the solution of Sherrington and Kirkpatrick. The low temperature phase does not have unphysical properties forT0, in contrast to previous investigations.     

Effect of the block-spin configuration on the location of βc in two-dimensional Ising modelsin two-dimensional Ising models

We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or –1) and these block spin values are kept fixed. We then impose the majority rule and look at the effect on the phase transition that was present in the original unconstrained spin system. We find that for the checkerboard block-spin configuration, Monte Carlo simulations show that _c is close to 1, which, compared to the original nearest neighbor Ising _c = 0.44..., shows that the critical temperature has been reduced by more than one half. For none of the other 11 block-spin configurations that we have considered is there any indication of a phase transition in the constrained system of original spins.     

Light-induced formation of metastable high-spin states in [Fe(mtz)6](CiO4)2

[Fe(mtz)₆](CiO₄)₂ (mtz=1-methyltetrazole) is a spin crossover compound with two different iron(II) lattice sites. Only one of them (lattice site A) shows thermally induced high spin (HS) low spin (LS) spin transition. The LIESST effect (Light-Induced Excited Spin State Trapping) can be observed below 50 K. Complex molecules in B-sites remain in HS state at all temperatures. At 20 K irradiation with red light causes a partial conversion to another HS species, HS(C), with also practically infinite lifetime.In partial fulfilment of the Ph.D. thesis.     

Numerical estimate of the phase diagram of finite ANNNI chains in transverse field

We have estimated numerically the phase diagram of a one dimensional spin 1/2 quantum Ising model with competing nearest and next nearest neighbour interactions in presence of a transverse field. The method essentially is to diagonalise exactly the Hamiltonian for finite (10 spins) open chains and calculate the spin-spin correlations from the ground state eigenvector. The results obtained confirm the transition between ferromagnetic and paramagnetic phases for <0.5 and between antiphase and paramagnetic phase for >0.5. ( is the ratio of next nearest and nearest neighbour interactions.) The results perhaps indicate furthermore that (i) there is a disorder line passing through =0.5; (ii) the zero point quantum fluctuations destroy the order near =0.5 as the transverse field is switched on; and (iii) there is probably also a floating phase with slowly decayling correlation near the order-disorder phase boundary for >0.5.     

Ground states of the Triangular Ising model with two-and three-spin interactions

The possible ground state spin configurations of an Ising model on a plane triangular lattice are investigated. The model incorporates competing interactions between spins at nearest and next-nearest neighbour sites as well as a coupling between three spins at the vertices of a nearest-neighbour triangle, and an external magnetic field. Models of this type are frequently used to describe the structures of adsorbate layers on hexagonal substrates. The analysis is based on linear inequalities involving the magnetization, two- and three-spin correlations, and on simple convexity arguments. Part of the inequalities needed are proved with the aid of a computer. For vanishing three-spin coupling the results of earlier studies are confirmed; in addition, the resulting seven topologically distinct structures are shown to be unique. Two of these structures are energetically degenerate; the degeneracy cannot be lifted by any further two-spin interaction. For nonzero three-spin coupling only an almost complete solution is given, involving four additional spin configurations. The ground state phase diagrams are discussed.     

Two-dimensional isotropic orientational glasses: a computer-simulation study

The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction.It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to ferromagnetic correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT0, and the critical exponents for this zero-temperature phase transition are estimated.Dynamic correlation functions are analyzed as well and it is shown that the dacay of spatially displaced correlations displays a Kohlrausch-Williams-Watts behavior similar to the self-correlation function of the quadrupole moments.Some quantities are compared to their corresponding counterparts on the threedimensional simple cubic lattice, which also has a zero-temperature transition but at corresponding temperatures has stronger short-range-order.     

Inhomogeneous Ising models with diagonal structure on a square lattice

We study 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 in diagonal direction. We calculate the partition function and free energy for a random coupling distribution of finite period. The phase transition is universally of Ising type. The transition temperature is independent of specific details of the coupling distribution. In particular, unexpected results for the absence of a phase transition are derived. Special examples are considered in detail, phase diagrams and critical temperature are determined. We calculate ground state energy and ground state degeneracy or, equivalently, rest entropy for pure frustration models, i.e. models with couplings of fixed strength but arbitrary sign, which never show a phase transition at a finite temperature.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln, FRG     

Inhomogeneous Ising models with diagonal structure on a square lattice

We study 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 in diagonal direction. We calculate the partition function and free energy for a random coupling distribution of finite period. The phase transition is universally of Ising type. The transition temperature is independent of specific details of the coupling distribution. In particular, unexpected results for the absence of a phase transition are derived. Special examples are considered in detail, phase diagrams and critical temperature are determined. We calculate ground state energy and ground state degeneracy or, equivalently, rest entropy for “pure” frustration models, i.e. models with couplings of fixed strength but arbitrary sign, which never show a phase transition at a finite temperature.     

Equilibrium Pure States and Nonequilibrium Chaos

We consider nonequilibrium systems such as the Edwards–Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken-symmetry pure states. Following a deep quench, we argue that as time t, although the system is usually in some pure state locally, either it never settles permanently on a fixed length scale into a single pure state, or it does, but then the pure state depends on both the initial spin configuration and the realization of the stochastic dynamics. But this latter case can occur only if there exists an uncountable number of pure states (for each coupling realization) with almost every pair having zero overlap. In both cases, almost no initial spin configuration is in the basin of attraction of a single pure state; that is, the configuration space (resulting from a deep quench) is all boundary (except for a set of measure zero). We prove that the former case holds for deeply quenched 2D ferromagnets. Our results raise the possibility that even if more than one pure state exists for an infinite system, time averages do not necessarily disagree with Boltzmann averages.     

Toom’s Model with Glauber Rates: An Exact Solution Using Elementary Methods

A simple spatially two-dimensional stochastic cellular automaton with asymmetric coupling and synchronous updating according to Glauber rates is considered. While detailed balance is violated it is still possible to compute analytically the stationary probability distribution by elementary means. The stationary distribution can be written as a canonical equilibrium distribution of a spin system on a triangular lattice with nearest neighbour coupling. Thus, the cellular automaton shows a nonequilibrium phase transition with Ising critical behaviour.     

Multicanonical sampling of the space of states of ℋ(2, <Emphasis Type="Italic">n</Emphasis>)-vector models

Problems of temperature behavior of specific heat are solved by the entropy simulation method for Ising models on a simple square lattice and a square spin ice (SSI) lattice with nearest neighbor interaction, models of hexagonal lattices with short-range (SR) dipole interaction, as well as with long-range (LR) dipole interaction and free boundary conditions, and models of spin quasilattices with finite interaction radius. It is established that systems of a finite number of Ising spins with LR dipole interaction can have unusual thermodynamic properties characterized by several specific-heat peaks in the absence of an external magnetic field. For a parallel multicanonical sampling method, optimal schemes are found empirically for partitioning the space of states into energy bands for Ising and SSI models, methods of concatenation and renormalization of histograms are discussed, and a flatness criterion of histograms is proposed. It is established that there is no phase transition in a model with nearest neighbor interaction on a hexagonal lattice, while the temperature behavior of specific heat exhibits singularity in the same model, in case of LR interaction. A spin quasilattice is found that exhibits a nonzero value of residual entropy.     

Characterisations of phase transitions in Ising spin systems

We construct aC*-algebraic formalism designed to provide a framework for the characterisation of phase transitions in a class of Ising spin systems: this class is large enough to include the rectangular lattice models, of arbitrary finite dimensionality, with nearest neighbour interactions. Using an extension of Onsager's transfer matrix formalism, we express properties of a Gibbs state of a system in terms of a contractive linear transformation, ₀, of a certain Hilbert space, the properties of ₀ being governed by the temperature as well as the interactions in the system. We obtain conditions on ₀ under which the system exhibits a phase transition characterised by (A) a thermodynamical singularity, (B) a change in symmetry, associated with theG-ergodic decomposition of Gibbs states, (C) a divergence of a correlation length (appropriately defined) at the critical point, and (D) scaling laws in the critical region. Applying our formalism to the rectangular two-dimensional Ising model with nearest neighbour interactions, we show that its phase transition possesses the properties (B) and (C), as well as (A).     

The spectrum of the transfer matrix in theC*-algebra of the Ising model at high temperatures

We investigate the state on the Fermion algebra which gives rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model on a half lattice with nearest neighbour interaction. It is shown that the operatorP ^– in the GNS space, which performs the essential functions of the renormalized transfer matrix, has a quasi-particle structure.     

Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.     

Square lattice Ising antiferromagnet in an external magnetic field

We study the anisotropic square lattice Ising antiferromagnet in terms of three parameters: an external magnetic field B, an effective temperature and an anisotropy parameterK. The model, i.e., partition function and free energy, is solved exactly in the anisotropic limit,K0, for arbitrary temperature and field by using the transfer matrix method. We also calculate the first corrections beyond this limit. The limit is non trivial and the phase transition is completely preserved. It is of the expected Ising type. The transition temperature _c (B, K) is determined exactly for bothK0 andK and the results are used to check the validity of a recently conjectured formula by Müller-Hartmann and the author.     

Monte Carlo study of the two-step spin transition in [FeXZn1∓X(2-pic)3]Cl2 · EtOH

The Monte Carlo method has been applied to reproduce the two-step spin transition in [Fe_xZn_1?x(2-pic)₃]Cl₂ · EtOH (2-pic = 2-picolylamine). The partition function of the Hamiltonian has been factorized in two parts describing the inner degrees of freedom of the spin transition molecules and the interaction between them. The factorization is equivalent to an effective Hamiltonian which can be mapped on an Ising system in an applied magnetic field. The interaction consists of an infinite range and a short range interaction part. Qualitatively the two-step transition under pressure and the Zn diluted system have been well reproduced with infinite range and the next nearest neighbour interaction of ferromagnetic type and the nearest neighbour interaction of antiferromagnetic type in a simple cubic lattice.     

Decimation transformations in lattice systems of continuous spins

Decimation renormalization transformations are investigated for systems of continuous spins. The usual arguments against decimation can be avoided by considering products of decimation and spin scaling transformations. With the simple local types of spin scaling normally used for continuous spins, even these product transformations will have no fixed points for lattice dimension greater than one. A Gaussian fixed point for one-dimensional models with short range (but not only nearest neighbor) interactions is exhibited. A series of scaling transformations of increasing generality is investigated. It is found that a product of a nonlocal spin scaling transformation and a decimation will produce the usual fixed points, but that this type of product transformation is effectively much more a block-type transformation than a pure decimation.     

Kosterlitz-Thouless transitions in simple spin-models with strongly varying vortex densities

A generalized XY-model, consisting of a family of nearest neighbour potentials of varying shape, for classical planar spins on a two-dimensional square lattice is analysed by a combination of Migdal-Kadanoff real-space renormalization and Monte Carlo simulations on a sequence of finite lattices of up to 256×256 spins. For all potential shapes, Kosterlitz-Thouless transitions are found with the same universal features as in the pure XY-model, whereas the density of vortices in the transition region depends strongly upon the shape of the potential.     

Ising-like field theory

A field theory model onR ² in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in of the ground state energy, as 0, without using the cluster expansion.Supported in part by Consiglio Nazionale delle Ricerche.