Transition order and dynamics of a model with competing exchange and dipolar interactions

We performed Monte Carlo simulation of phase transitions from isotropic stripe phase with short-range order to long-range stripe phase in a model with competing ferromagnetic exchange and antiferromagnetic dipolar interactions on triangular lattice. We calculated phase diagram for different values of exchange and dipolar interaction constants ratio, η. We also determined the order of the transitions to stripe phases AFh of different stripe widths h: first-order phase transition was found to transitions into AF1 and AF2 phases, while transitions to AF3 and AF4 phases were of the second order. In the phase diagram the tricritical point was determined at the AF2 and AF3 phase boundary. We observed the peak of nematic phase at the transition region to the AF1 phase, but found it metastable at low values of η. We have also found that in AF1 phase spin relaxation corresponds to the Ising model dynamics. In phases AF3 and AF4 the dynamics slows down, and stripe domain growth with time is proportional to logt.     

Arrested states formed on quenching spin chains with competing interactions and conserved dynamics

We study the effects of rapidly cooling to T=0 a spin chain with conserved dynamics and competing interactions. Depending on the degree of competition, the system is found to get arrested in different kinds of metastable states. The most interesting of these has an inhomogeneous mixture of interspersed active and quiescent regions. In this state, the steady-state autocorrelation function decays as a stretched exponential approximately exp[-(t/tau(0))(1/3)], and there is a two-step relaxation to equilibrium when the temperature is raised slightly.     

Lattice gas models with competing interactions

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.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

Spin configurations in hexagonal antiferromagnets with competing interactions

The ordered phase of the most part of ABX₃ antiferromagnets appears as a stacking of 120°-three sublattice spin layers with alternate spin direction along thec-axis. This configuration is easy to be explained because it is the minimum energy configuration of the Heisenberg hexagonal model with nearest neighbour antiferromagnetic interaction. However we show that moderate competitive interactions between in plane next nearest and third nearest neighbours stabilize incommensurate spin configurations. This gives some insight into the unexplained spin configuration observed in RbMnBr₃ by elastic neutron scattering experiment.     

Frustration without competing interactions

The concept of frustration is investigated following an idea of Anderson. A simple, frustrated in Anderson's sense, nonrandom classical lattice spin system without competing interactions is discussed, which exhibits infinitely many equilibrium states at low temperature. The overlap distribution function is calculated exactly to be a delta function at zero.     

Corrections to scaling in disordered systems with competing interactions

Using a mean-field effective-field model for disordered systems with competing interactions we have (a) obtained explicit expressions for the corrections to scaling for both ferromagnets and spin glasses up to order h³ in the magnetization, and (b) performed numerical calculations of the non-linear susceptibility of both ferromagnets and spin glasses as a function of reduced field and temperature. Scaling plots constructed from the numerical data show that the departures from universality are much more significant for spin glasses than they are for ferromagnets and that, while the discrepancy can be reduced through a redefinition of the scaling variables, a knowledge of the proper non-universal scaling correction is essential for spin glasses if a reasonable degree of universality is to be achieved.     

Stripe melting in a two-dimensional system with competing interactions

A model with competing short-ranged attractions and long-ranged repulsions that describes self-organized patterns in systems like Langmuir monolayers, magnetic films, and adsorbed monolayers is studied using numerical simulations and analytic theory. Simulations provide strong evidence confirming that the stripe phase order is destroyed in a defect unbinding transition. Large scale computer simulations are in agreement with an analytic scaling theory, which also predicts an eventual crossover from defect-mediated stripe melting to a spin-disordering (or particle-mixing) mechanism with decreasing repulsion strength.     

Phase diagrams of Ising films with competing interactions

The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film thickness. The robustness of the phase diagrams against varying the couplings in the surface layers is analysed. Received 19 March 2002 and Received in final form 2 April 2002 Published online 6 June 2002     

Magnetic phase transitions in amorphous systems with competing exchange interactions

A method is proposed for analyzing magnetic phase transitions within the Ising model under the conditions of competing direct and indirect exchange interactions. It is demonstrated that the competition of exchange interactions leads to a reentrant phase transition between the ferromagnet and spin glass near the percolation threshold below the Curie temperature.     

Spin ordering in three-dimensional crystals with strong competing exchange interactions

In this paper we discuss magnetic ordering in three-dimensional crystals in which Heisenberg exchange interactions appear to dominate. Particular emphasis is placed on systems with strong competing exchange interactions, called frustrated spin systems. In the absence of such competition, one finds collinear spin ordering. However, strong competing interactions lead to non-collinear structures, often spirals and many variations thereof. The problem of understanding the origin and physical properties of such spin states within the classical Heisenberg model has been intensively addressed by a large community of researchers over the last 2–3 decades. The study of such problems actually began about five decades ago, and led to a large body of literature that has been overlooked in the publications of the last 2–3 decades (with two very recent exceptions). The early work established important fundamental concepts, including an unconventional theoretical approach, the generalized Luttinger–Tisza method and the idea of forced degeneracy. This resulted in the spin state called a ferrimagnetic spiral (FS), which enabled understanding of puzzling neutron diffraction data, plus NMR and ESR measurements, on the spinels XCr₂O₄, X?=?Mn, Co. Additional new aspects of this magnetic ordering have been uncovered in two very recent experimental works, indicating a partial spin-liquid-like behaviour and production of ferroelectricity by the pure spiral component of the FS. This exciting relevance of the early work to these modern results and the general lack of awareness of the early work has provided a source of motivation for this review, which covers that early body of work, both theoretical and experimental, and which also connects to the recent studies. A thorough discussion of the calculations, and comparison with experiments is presented. It will be seen that fundamental puzzles remain for these systems.     

Absence of spontaneous magnetization in spin systems with competing interactions

It is rigorously proved that spontaneous magnetization is absent in disordered spin systems if the strength of interaction is distributed symmetrically around a vanishing mean value, as a consequence of local gauge symmetry. This result is extended also to asymmetric distributions. A comment is made on gauge symmetry and frustration in quantum spin systems.     

Intermolecular spin-spin interactions in liquids

Kinetic equations for the one-particle spin density matrix for a system of magnetic molecules in a liquid interacting with one another through intermolecular spin-spin forces are derived under the following assumptions: a) “internal” relaxation processes are ignored: b) at t = 0 the entire density matrix is factorized,$\text{σ}\text{(0) = Π}{}_1\text{σ}{}_1\text{(0),}\text{σ}\text{(0)}$ being the spin density matrix of the matrix of the with molecule; c) random motions of particles in the liquid are considered as a classical markovian process. The finite set of integrodifferential equations, with rank equal to the number of different kinds of the molecules, is obtained for the matrices $\text{〈}\text{σ}{}_1\text{(t)〉}$ averaged over all the possible trajectories of the molecules in the liquid.The equation of motion for the magnetic moment, nonlinear in magnetization, is written for a system of identical molecules with $\text{S =}\text{1}\text{2}$ in the low-concentration limit. This equation is used to investigate the form of the equilibrium magnetization-recovery curve.     

Ising model with competing interactions on a Cayley tree

An iterative scheme is developed for a renormalized effective nearest-neighbor couplingK _r and effective field per siteK _r for spins in therth shell of a Cayley tree with nearest neighborJ, and next nearest neighborJ′, interactions between Ising spins on the lattice. In addition to the expected paramagnetic, ferromagnetic, and antiferromagnetic phases, we find an intermediate range ofJ'/J < 0 values whereX _r, and K_r iterate to a continuous or quasicontinuous attractor in theX-K plane. In this range the local magnetization is mainly chaotic with oscillatory glasslike behavior. Embedded in the chaos, however, are regions of periodic and commensurate phases.     

Ground-state energy of a quantum chain with competing interactions

We show rigorously that the ground state of a quantum chain with competing ferromagnetic nearest and antiferromagnetic next nearest interactions undergoes a transition from ferromagnetic to helical type, in the isotropic case, for a certain value of the relevant ratio of coupling constants. Boundaries of the phase diagram are also determined in the anisotropic case. The stability of a special quantum state (corresponding to a classical modulated phase of =/3) is analyzed by an extension of Holstein-Primakoff arguments, along a line of constant ratio of couplings, showing in particular a sequence of (instability) gaps. Finally, a natural adaptation of a variational wave function due to Huse and Elser is used to study several portions of the phase diagram, with very good agreement with previous theoretical results.