Stochastic resonance and scale invariance in nonequilibrium metastable states

Using computer simulations, we study metastability in a two-dimensional Ising ferromagnet relaxing toward a nonequilibrium steady state. The interplay between thermal and nonequilibrium fluctuations induces resonant and scale-invariant phenomena not observed in equilibrium. In particular, we measure noise-enhanced stability of the metastable state in a nonequilibrium environment. The limit of metastability, or pseudospinodal separating the metastable regime from the unstable one, exhibits reentrant behavior as a function of temperature for strong nonequilibrium conditions. Furthermore, when subject to both open boundaries and nonequilibrium fluctuations, the metastable system decays via well-defined avalanches. These exhibit power-law size and lifetime distributions, resembling the scale-free avalanche dynamics observed in real magnets and other complex systems. We expect some of these results to be verifiable in actual (impure) specimens.     

Dynamic light scattering in solid polymers

The viscosity of an amorphous polymeric solid above its glass transition [T _g (T,P)] increases as the temperature of the solid is decreased or the pressure is increased. Under changes in temperature or pressure, molecular subunits in the polymeric solid undergo configurational changes. Such changes or relaxations have a distribution of relaxation strengths and times. As the solid is cooled or as the hydrostatic pressure on the solid is increased, the relaxation strengths increase and the relaxation times increase. These changes in relaxation or dynamic properties are very dramatic as the empirical T _g is approached. Near T _g the polymeric solid is no longer in volume equilibrium; continued cooling or pressuring at a time rate faster than the average relaxation time will produce a polymeric glass. This glass is a nonequilibrium, amorphous solid. If the glass is held at a fixed temperature and pressure very close to, but below, T _g , the volume of the glass will be observed to relax to its equilibrium value. For temperatures and pressures well below T _g , equilibrium is a much more conjectural concept since the relaxation times become extremely long. It has been proposed^1,2 that there is a characteristic temperature T _g at which an amorphous polymer undergoes a second-order transition to an equilibrium glass with zero configurational entropy (i.e., a noncrystallizable solid).     

Cavitation in water: a review

Liquid water can be brought beyond the liquid–vapor equilibrium line into a metastable state, before nucleation of bubbles (cavitation) occurs. We review the experimental work on cavitation in water, focusing on the determination of the ultimate degree of metastability at which liquid water can exist. We also present practical applications of metastability and cavitation. To cite this article: F. Caupin, E. Herbert, C. R. Physique 7 (2006).     

Supercooling across first-order phase transitions in vortex matter

Hysteresis in cycling through first-order phase transitions in vortex matter, akin to the well-studied phenomenon of supercooling of water, has been discussed in literature. Hysteresis can be seen while varying either temperature T or magnetic field H (and thus the density of vortices). Our recent work on phase transitions with two control variables shows that the observable region of metastability of the supercooled phase would depend on the path followed in H-T space, and will be larger when T is lowered at constant H compared to the case when H is lowered at constant T. We discuss the effect of isothermal field variations on metastable supercooled states produced by field-cooling. This path dependence is not a priori applicable to metastability caused by reduced diffusivity or hindered kinetics.     

Magnetic X-ray scattering study of random field effects in Mn0.75Zn0.25F2

We report a detailed synchrotron X-ray scattering study of the magnetic correlations in two samples of Mn_0.75Zn_0.25F₂ as a function of temperature and applied field. The critical behavior of this system is believed to be isomorphic with that of the three-dimensional random field Ising model (RFIM). On cooling in an external magnetic field (FC), the first sample exhibits a transition to long range order (LRO) in the near-surface region, at a field dependent temperature,T _N (H). In contrast, bulk neutron scattering studies show a long lived metastable domain state forming below a metastability boundary,T _M (H). The transition temperatureT _M (H), lies below the metastability boundary,T _M (H). The temperature difference,T _M (H)–T _M (H), increases with increasing field and agrees closely with the value deduced from an extrapolation from aboveT _M (H) of earlier, equilibrium neutron scattering results on the spin-spin correlation length. On cooling, the order parameter exponent is found to be large, =0.30±0.05. We speculate that there is an imbalance in the random fields in the neighborhood of linear surface defects (scratches) in this sample, and that the consequent net staggered field initiates a regular random Ising transition. The second sample was cut from the first and underwent a more extensive polishing process, resulting in a smoother surface with a small density of visible defects. Interestingly, it does not attain a LRO state on cooling, but rather it forms a domain state consistent with that observed by neutron diffraction. Both samples may be prepared in a LRO state, either by cooling in zero field and subsequently applying a field (ZFC) or, at high fields, by heating from the XY phase (FHXY). We have studied the evolution of the metastable LRO state in each sample on warming. We find universal behavior in both samples at all fields studied. Specifically there is a powerlaw-like decay of the order parameter with exponent =0.20±0.05, and a rounded transition region which may be described by a Gaussian distribution of transition temperatures. The width of this distribution scales asH ². A scaling plot of all the warming data as a function of the scaling variable (T–T _C (H)/H ² is constructed. We label this non-equilibrium pseudo-critical behavior, trompe l'oeil critical behaviour. Phenomenologically, these results enable us to explain many previous, apparently contradictory, results in the literature.     

Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions

We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T 0, h 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.     

Hysteresis phenomena in charging of Si Mosfet in quantizing magnetic field

We report the observation of nonequilibrium processes of charging in 2D electron layer in Si MOSFET. There were investigated the hysteresis variations of a 2D-layer charge Q_S with a gate voltage V_g or with a magnetic field H, and the hysteresis of a gate potential U_g vs magnetic field at Q_S = Const. At sufficiently low temperature T < 1K the relaxation time of a nonequilibrium state is much higher than 10³ sec. The observed phenomena may be explained qualitatively in frame of a surface potential randomness conception.     

The bicritical phase diagram of two-dimensional antiferromagnets with and without random fields

Neutron scattering measurements have been made of the phase diagrams of the nearly two-demensional antiferromagnets Rb₂MnF₄ and Rb₂Mn_0.7Mg_0.3F₄ in a magnetic field applied along thec-axis. In Rb₂MnF₄ there is at low temperatures a spin-flop phase at fields above 5.5 T which has long range order. The observation of true long range order rather than the algebraic decay of the order characteristic of the two-dimensional XY model is presumably due to subtle anisotropy effects in the plane as well as weak three-dimensional coupling. The phase boundaries of the uniaxial and transverse phases are shown to be consistent with renormalization group predictions for two-dimensional systems. The two lines become exponentially close to each other at low temperatures. The weak three-dimensional coupling moves the bicritical point fromT=0 to a non-zero temperature. The situation is more complex in Rb₂Mn_0.7Mg_0.3F₄ because of Ising random field effects. At low fields we observe typical random field metastable behavior with a sharp metastability boundary and a gange of length scales which are time independent below that boundary. At higher fields there are substantial uniaxial fluctuations. The transverse phase boundary and the metastability line appear to intercept atT=0 showing that the random field fluctuations do have a large effect on the phase diagram. The theory of the phase diagrams has been extended to include the random field fluctuations and good agreement is obtained with the observed transverse phase boundary. Unfortunately, there is as yet no theory of the metastable uniaxial phase with which to compare our results.     

Some previously unexpected phenomena of volume recovery

We have extensively studied the nonequilibrium behavior of atactic polystyrenes in a broad range of temperatures. Depending on the conditions of the initial temperature (To) and the aging temperature (T), the shapes of isotherms plotted in the form of total fractional free volume (viz., δ) versus logarithmic aging time can be linear or nonlinear. At a T in the vicinity of T_g , the isotherms converge together. When the Tis lowered, the isotherms become increasingly nonlinear; eventually, these isotherms intersect one another at various points, forming a newly discovered crossing phenomenon. Differences in volume contraction persist throughout further aging, regardless of the equality in δ right at the moment of crossing. In a further case, the nonlinear isotherms between the two polystyrenes may be superposable by a simple δ shift, despite their substantial differences in δ. As none of these phenomena can be justified by kinetic arguments, this study seriously questions the validity of the existing kinetic theories as well as the existence of the extrapolated underlying equilibrium state.     

The kinetics of relaxation of magnetization fluctuations near the phase transition from paramagnetic state to ferromagnetic state with domain structure

The equations of motion describing relaxation of magnetization fluctuations in the paramagnetic state for a uniaxial ferromagnet have been solved. In the Landau-Ginzburg functional the demagnetization energy has been taken into account. The finite dimensions of a sample have been considered. It has been shown, that a phase transition is generated by fluctuations containing information about the period of the domain structure at the phase transition point T_c¹. The obtained formulae describe T_c¹ and the period of the domain structure. The results can be used both for bulk materials and thin films.     

Towards a Theory of Transition Paths

We construct a statistical theory of reactive trajectories between two pre-specified sets A and B, i.e. the portionsof the path of a Markov process during which the path makes a transition from A to B. This problem is relevant e.g. in the context of metastability, in which case the two sets A and B are metastable sets, though the formalism we propose is independent of any such assumptions on A and B. We show that various probability distributions on the reactive trajectories can be expressed in terms of the equilibrium distribution of the process and the so-called committor functions which give the probability that the process reaches first B before reaching A, either backward or forward in time. Using these objects, we obtain (i) the distribution of reactive trajectories, which gives the proportion of time reactive trajectories spend in sets outside of A and B; (ii) the hitting point distribution of the reactive trajectories on a surface, which measures where the reactive trajectories hit the surface when they cross it; (iii) the last hitting point distribution of the reactive trajectories on the surface; (iv) the probability current of reactive trajectories, the integral of which on a surface gives the net average flux of reactive trajectories across this surface; (v) the average frequency of reactive trajectories, which gives the average number of transitions between A and B per unit of time; and (vi) the traffic distribution of reactive trajectories, which gives some information about the regions the reactive trajectories visit regardless of the time they spend in these regions.     

Relaxation modes in glassy polymers: A temporal analysis by the simplex method of isothermal depolarisation current measurements

Molecular dynamics associated to relaxation phenomena in the glass transition temperature domain is often investigated by means of thermostimulated depolarisation current TSDC technique. It is a very sensitive method and the data are traditionally obtained according to two protocols leading to the well known complex spectra and elementary spectra. The aim of this work is to use a new TSDC protocol which analyses the relaxation current kinetics obtained after submitting the sample to an electrical field pulse at a constant temperature. A new temporal analysis of the return equilibrium isothermal transient current I(T) is proposed. The signal fitting is obtained by a simplex optimisation method. The entire signal recorded for all the temperatures can be fitted with a sum of two exponentials allowing the definition of two different relaxation times called τ₁ and τ₂. This new protocol has been used to analyse the glass transition domain of amorphous PET.     

Random‐field ising systems: A survey of current theoretical views

Ising or Ising-like models in random fields are good representations of a large number of impure materials. The main attempts of theoretical treatments of these models--as far as they are relevant from an experimental point of view--are reviewed. A domain argument invented by Imry and Ma shows that the long-range order is not destroyed by weak random-fields in more than D = 2 dimensions. This result is supported by considerations of the roughening of an isolated domain wall in such systems: domain walls turn out to be well defined objects for D > 2, but arbitrarily convoluted for D < 2. Different approaches for calculating the roughness exponent ζ yield ζ= (5 - D)/3 in random-field systems. The application of ζ in incommensurate-commensurate critical behaviour is discussed.

Non-classical critical behaviour occurs in random-field systems below D = 6 dimensions which is determined in general by three independent exponents. The new exponent y_J = θ= D/2 - σ corresponds to random-field renormalization or, to say it differently, to the irrelevance of the temperature at the zero-temperature fixed point, which is believed to rule the critical behaviour. The inequalities satisfied by these exponents are investigated, as well as the relations between the eigenvalue and the critical exponents and their numerical values found in the literature.

Domain wail roughening due to random fields produces also metastability and hysteresis. It is shown that when cooling a 3D system into the low-temperature phase in an applied random field, the system runs into a metastable domain state, in agreement with the experimental observation. The further approach of the system to the ordered equilibrium state is hindered by pinning which leads to domain size increasing only logarithmically in time. Domain wall roughness and pinning in random bond systems is also considered.     

Structural relaxation investigations of glassy polystyrene by radial distribution functions

The structural relaxation of an atactic polystyrene under sub-T _g annealing at 50°C and at 70°C was investigated by the radial distribution function (RDF) derived from its wide-angle x-ray scattering (WAXS). By recording the changes in RDF (i.e., ΔH(r), where r is the radial distance from an arbitrary reference atom) after it had been annealed for a certain period of days, and taking the integration of ΔAH(r) ²dr, we found that the atom density within structural domains in a size below 15 Å was changed dramatically, but that the tendency leveled off as annealing proceeded. However, the atom density outside the domains is barely changed by sub-T _g annealing. The size of the domain is similar to the statistical segment length reported in the literature. The behavior of the domains—that the segmental relaxation inside the domains in the initial sub-T _g annealing is unconstrained by their neighbors outside the domains—is also similar to the behavior of the statistical segments. The domains are believed to be composed of a statistical segment across the center, which has about 6 styrene repeat units, and 6 equal-distanced parallel segments tangent to the edge of the domain. On the other hand, as the annealing temperature is closer to the glass transition temperature, the frozen unstable chain segments reach equilibrium sooner and with less disturbance in their conformation.     

Dynamical behavior of muonium on silica surfaces

The behavior of muonium on the surface of finely divided silica (amorphous SiO₂) powder (mean grain diameter 70 Å) has been studied as a function of the surface concentration of hydroxyl groups. The temperature dependence of the Mu relaxation rate in transverse field was measured for samples prepared with 0%, 50% and 70% of the surface hydroxyl groups removed over the temperature range 4 K <T < 300 K. The relaxation rate shows a distinct maximum at about 25 K and a minimum at about 16 K for all three samples, and shows a dramatic decrease below 16 K as the concentration of surface hydroxyls is reduced. A three-state nonequilibrium model describing the diffusion and trapping of muonium on the silica surface is used to interpret the data.On leave from Department of Physics, University of Saskatchewan, Saskatoon, Sask. S7N OWO, Canada.     

Thermal Relaxation of a QED Cavity

We study repeated interactions of the quantized electromagnetic field in a cavity with single two-levels atoms. Using the Markovian nature of the resulting quantum evolution we study its large time asymptotics. We show that, whenever the atoms are distributed according to the canonical ensemble at temperature T>0 and some generic non-degeneracy condition is satisfied, the cavity field relaxes towards some invariant state. Under some more stringent non-resonance condition, this invariant state is thermal equilibrium at some renormalized temperature T ^*. Our result is non-perturbative in the strength of the atom-field coupling. The relaxation process is slow (non-exponential) due to the presence of infinitely many metastable states of the cavity field.     

One-and two-front states of equilibrium in a thin superconducting film

Two-phase states of equilibrium of a thin superconducting film carrying a current under conditions of convective heat exchange at the free surface of the film are studied. It is shown that for a classical superconductor the two-phase state of the film remains a single-front state over a wide range of parameters of the system. For high-T _c superconductors there exists a maximum value of the Steckl number above which weakly nonequilibrium stationary states can only be multifront states. The solutions of the boundary-value problem modeling a two-front state of equilibrium are investigated, and the conditions under which they obtain are examined. Zh. Tekh. Fiz. 68, 84–87 (March 1998)     

Relaxation properties in classical diamagnetism

It is an old result of Bohr that, according to classical statistical mechanics, at equilibrium a system of electrons in a static magnetic field presents no magnetization. Thus a magnetization can occur only in an out of equilibrium state, such as that produced through the Foucault currents when a magnetic field is switched on. It was suggested by Bohr that, after the establishment of such a nonequilibrium state, the system of electrons would quickly relax back to equilibrium. In the present paper, we study numerically the relaxation to equilibrium in a modified Bohr model, which is mathematically equivalent to a billiard with obstacles, immersed in a magnetic field that is adiabatically switched on. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the Fermi Pasta Ulam problem is also pointed out.     

Nonequilibrium wetting transition in a nonthermal 2D Ising model

Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E _c . Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.