Rigorous results concerning a generalized mean-field theory of dilute disordered Ising magnets

A nonlinear integral equation describing the distribution of the internal random field in a disordered Ising system under conditions appropriate to describe a spin-glass is studied.Using the principle of contraction mapping it is shown that the equation has one and only one solution over a finite range of temperatures, corresponding to a nontrivial transition to a spin-glass type state.     

Low-temperature metastable states in a stacked triangular Ising antiferromagnet

We study low-temperature magnetization processes in a stacked triangular Ising antiferromagnet by Monte Carlo simulations. In increasing and decreasing magnetic fields we observe multiple steps and hysteresis corresponding to formation of different metastable states. Besides the equidistant threefold splitting of the 1/3 ferrimagnetic plateau, we additionally confirm a fourth plateau in the field-increasing branch and a sizable remanence when the field is decreased to zero. The newly observed plateau only appears at sufficiently low temperature and sufficiently large exchange interaction in the stacking direction. These observations reasonably reproduce low-temperatures measurements on the spin-chain compound Ca₃Co₂O₆.     

Decay kinetics of metastable states in a disordered linear system

Kolmogorov’s method for describing statistical crystallization is generalized to take into account disorder in the structure and is applied to the calculation of the decay kinetics of metastable states in linear (in the sense of spatial dimensionality) systems. The theory describes the influence of defects on the dynamics of polymers and domain boundaries between phases on substrates, on crystal growth involving the movement of steps over a surface, on the plastic flow of materials due to the motion of dislocations in a Peierls-Nabarro relief, and on the kinetics of other physical systems. Fiz. Tverd. Tela (St. Petersburg) 41, 1988–1993 (November 1999)     

On the theory of metastable states

It is shown that the stationary states of stochastic systems are stable. Therefore one cannot use the stationary probability distributions for describing the stochastic systems in metastable states. It is shown that the nonstationary stochastic processes can have sample paths with stationary parts. It is proposed to consider these stationary parts as the metastable states.     

Stochastic theory of metastable states and nucleation

We study on a model the role of fluctuations size in the nucleation of a first order phase transition. A bifurcation point exists between metastable and stable equilibrium solutions for a critical value of fluctuations size.     

Macroscopic theory of activated decay of metastable states

The Brownian motion of a particle over a potential barrier, a problem first solved by Kramers, is reexamined also for the case of intermediate friction, to which Kramers' solutions do not apply. The theory is macroscopic and entirely based on the Langevin equation of the particle, but it makes essential use of ideas of a recent microscopic theory of Grabert and of Pollak, Grabert, and Hänggi for a particle coupled to an infinite set of harmonic oscillators. Their result for the escape rate is recovered, but the present method seems more generally applicable. We introduce and use a new theoretical tool-the transformation to a new set of variables mixing the macroscopic and the noise variables of the Langevin equation.     

Organization and energy properties of metastable states for the random-field Ising model

Random-field Ising model (RFIM) systems are characterized by a large number of metastable states corresponding to local minima of the system energy with respect to single spin flip. We classified the minima in a hierarchical way based on the possibility of a given state to escape from a basin of mutually reachable states. We investigate the energy properties of the metastable states in relation to the basin they belong to: states of particularly high energy, obtained by fast-quenching randomly initial spin configurations, tend to have access to a complex structure of correlated basins, opposite to what is found for low-energy states. The purpose of this paper is to investigate the connection between the properties of the basin oriented graph and the energy of the corresponding states.     

New effective-field theory with correlations; application to disordered magnets

The Ising model of spin 1/2 with nearest-neighbour interaction is investigated. Within the effective-field theory introduced by Honmura and Kaneyoshi, a new type of decoupling approximation is introduced for treating the multispin correlation functions. The critical temperature, the spontaneous magnetization, and the two-site spin c correlation function are calculated for a two- (or three-) dimensional lattice. The present formalism yields results better than those of Bethe-Peierls approximation and is extended to disordered magnets. The thermodynamical quantities of quenched random-bond magnets, such as magnetization, susceptibility and so on, are studied, We find that in particular the twosite spin correlation functions of the disordered magnets exhibit some interesting behavior.     

NMR dynamics in disordered magnets

The excitation dynamics of site diluted magnets can be described at low energies (long length scales) by magnons, and above a crossover frequency, ω_c, (short length scales) by fractons. The density of fracton states is given by , where is the fracton dimensionality. Dilution gives rise to a characteristic length ξ∝(p−p _c)^ν, wherep _c is the critical concentration for (magnetic) percolation. The crossover frequency ω_c is proportional to ξ^-1[1+(θ/2)], where θ is the rate at which the diffusion constant decays with distance for diffusion on an equivalent network. A fractal dimensionD describes the density of magnetic sites on the infinite network, and . For percolating networks, for all dimensions ≥2. Neutron scattering structure factor measurements by Uemura and Birgeneau compare well with calculations using fracton concepts. Magnons are extended at low energies, while the fracton states are geometrically localized, with a wave function envelope proportional to exp . Here, is the fracton length scale at frequency ω. The exponentd _ϕ lies between 1 andd _min, the chemical length index (of the order of 1.6 in three dimensions). The localization of the magnetic excitations causes a spread in the NMR relaxation rates. A given nuclear moment will experience only a limited set of fracton excitations, resulting in an overall non-exponential decay of the NMR relaxation signal. When strong cross-relaxation is present, the relaxation will be exponential, but the temperature dependence will be strongly altered from the concentrated result.     

Gauge model of disordered magnets

A model of disordered magnets with their ground state degenerate in energy is proposed. It is shown that the presence of singularities in the field of an order parameter leads to the appearance of additional degrees of freedom described by the gauge field of the rotation group. The gauge fields arise as coefficients of the connection of some non-trivial fibre bundle. The lagrangian of disordered magnets with linear singularities (disclinations) in the field of the order parameter is constructed, and the spectrum of hydrodynamic modes is found.     

Multiplicity of metastable nonergodic states of a dispersed nonwetting liquid in a disordered nanoporous medium

Three different metastable nonergodic states of a dispersed nonwetting liquid (water) in the Fluka 100 C8 and Fluka 100 C18 disordered porous media, as well as transitions between these states under variation of the temperature and the degree of filling, have been qualitatively described. It has been shown that the appearance of such states is due to spatial variations of the number of the nearest neighbors because of the broadening of the pore size distribution function f(R), fluctuations of various local configurations of neighbors in the system of pores, and fluctuations of a configuration of a pore and its environment consisting of filled and empty pores on a percolation cluster. These states and transitions are caused by the competition between the effective repulsion of the nonwetting liquid from the wall of the pore, which is responsible for the “extrusion” of the liquid from the pore, and the effective collective multiparticle attraction of the liquid cluster in the pore to clusters in the neighboring connected pores. The theoretical dependences obtained make it possible to qualitatively describe experimental data.     

Rigorous treatment of metastable states in the van der Waals-Maxwell theory

We consider a classical system, in a ν-dimensional cube Ω, with pair potential of the formq(r) + γ ^v φ(γr). Dividing Ω into a network of cells ω₁, ω₂,..., we regard the system as in a metastable state if the mean density of particles in each cell lies in a suitable neighborhood of the overall mean densityρ, withρ and the temperature satisfying $$f_0 (\rho ) + \tfrac{1}{2}\alpha \rho ^2 > f(\rho ,0 + )$$ and $$f''_0 (\rho ) + 2\alpha > 0$$ wheref(ρ, 0+) is the Helmholz free energy density (HFED) in the limit γ→ 0; α = ∫ φ(r)d ^v r andf ₀ (ρ) is the HFED for the caseφ = 0. It is shown rigorously that, for periodic boundary conditions, the conditional probability for a system in the grand canonical ensemble to violate the constraints at timet > 0, given that it satisfied them at time 0, is at mostλt, whereλ is a quantity going to 0 in the limit $$|\Omega | \gg \gamma ^{ - v} \gg |\omega | \gg r_0 \ln |\Omega |$$ Here,r ₀ is a length characterizing the potentialq, andx ? y meansx/y → +∞. For rigid walls, the same result is proved under somewhat more restrictive conditions. It is argued that a system started in the metastable state will behave (over times ?λ ^?1) like a uniform thermodynamic phase with HFED f₀(ρ) + 1/2αρ², but that having once left this metastable state, the system is unlikely to return.     

Bose-glass phases in disordered quantum magnets

In disordered spin systems with antiferromagnetic Heisenberg exchange, transitions into and out of a magnetic-field-induced ordered phase pass through unique regimes. Using quantum Monte Carlo simulations to study the zero-temperature behavior, these intermediate regions are determined to be Bose-glass phases. The localization of field-induced triplons causes a finite compressibility and, hence, glassiness in the disordered phase.     

Resonances,metastable states and exponential decay laws in perturbation theory

Resonances which appear as perturbed bound states are discussed in the framework of Balslev-Combes theory. The corresponding metastable states are constructed using the formal perturbation expansion to orderN–1 for the (nonexistent) perturbed bound states. They are shown to have exponential decay in time governed by the complex resonance energies, up to a background of order 2N in the perturbation parameter. The results apply in lowest orderN=1 to the perturbation of bound states embedded in the continuum and in arbitrary order to cases like the Stark effect.Dedicated to Res Jost and Arthur Wightman     

Nonresonance spin-lattice absorption of ultrasound in Ising magnets

A theory of nonresonant acoustic absorption in Ising magnets is constructed by the nonequilibrium statistical operator method. It is assumed that the spins are coupled with the sound via modulation of the Ising exchange integral, and the nonresonant absorption is due to the interaction of the spin system with the thermal vibrations of the lattice. The frequency dependence of the absorption χ″(ω), which has an analytical form different from that of the well-known Debye function, is determined. The temperature dependence of χ″(ω), which is made up of 1) the averages of the vibrational variables and 2) the temperature dependence of the spin correlation functions of the linear Ising model, is analyzed. It is shown that the cross-coupling of the two subsystems (Ising and Zeeman) produces a second absorption peak at low frequencies together with the peak characteristic of the Debye curve. Fiz. Tverd. Tela (St. Petersburg) 39, 516–521 (March 1997)