A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0

We present a formalism for computing the complexity of metastable states and the zero-temperature magnetic hysteresis loop in the soft-spin random-field model in finite dimensions. The complexity is obtained as the Legendre transform of the free-energy associated to a certain action in replica space and the hysteresis loop above the critical disorder is defined as the curve in the field-magnetization plane where the complexity vanishes; the nonequilibrium magnetization is therefore obtained without having to follow the dynamical evolution. We use approximations borrowed from condensed-matter theory and based on assumptions on the structure of the direct correlation functions (or proper vertices), such as a local approximation for the self-energies, to calculate the hysteresis loop in three dimensions, the correlation functions along the loop, and the second moment of the avalanche-size distribution.Comment: 28 pages, 12 figure

The T=0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T=0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean-field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is positive everywhere inside). On the other hand, the occurence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied field, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.Comment: 29 pages, 9 figure

Critical behavior of a Ginzburg-Landau model with additive quenched noise

We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model subjected to quenched additive noise, which has been used recently as a framework for analyzing collective effects induced by diversity. We first make use of a self-consistent theory to calculate the phase diagram of the system, predicting the onset of an order-disorder critical transition at a critical value {\sigma}c of the quenched noise intensity \sigma, with critical exponents that follow Landau theory of thermal phase transitions. We subsequently perform a numerical integration of the system's dynamical variables in order to compare the analytical results (valid in the thermodynamic limit and associated to the ground state of the global Lyapunov potential) with the stationary state of the (finite size) system. In the region of the parameter space where metastability is absent (and therefore the stationary state coincide with the ground state of the Lyapunov potential), a finite-size scaling analysis of the order parameter fluctuations suggests that the magnetic susceptibility diverges quadratically in the vicinity of the transition, what constitutes a violation of the fluctuation-dissipation relation. We derive an effective Hamiltonian and accordingly argue that its functional form does not allow to straightforwardly relate the order parameter fluctuations to the linear response of the system, at odds with equilibrium theory. In the region of the parameter space where the system is susceptible to have a large number of metastable states (and therefore the stationary state does not necessarily correspond to the ground state of the global Lyapunov potential), we numerically find a phase diagram that strongly depends on the initial conditions of the dynamical variables.Comment: 8 figure

Liquid-liquid coexistence in the phase diagram of a fluid confined in fractal porous materials

Multicanonical ensemble sampling simulations have been performed to calculate the phase diagram of a Lennard-Jones fluid embedded in a fractal random matrix generated through diffusion limited cluster aggregation. The study of the system at increasing size and constant porosity shows that the results are independent from the matrix realization but not from the size effects. A gas-liquid transition shifted with respect to bulk is found. On growing the size of the system on the high density side of the gas-liquid coexistence curve it appears a second coexistence region between two liquid phases. These two phases are characterized by a different behaviour of the local density inside the interconnected porous structure at the same temperature and chemical potential.Comment: 5 pages, 4 figures. To be published in Europhys. Letter

Influence of the driving mechanism on the response of systems with athermal dynamics: the example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local-mean field theory at finite temperature (but neglecting thermallly activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model (RFIM) when controlling either the external magnetic field $H$ or the extensive magnetization $M$. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the $H$-driven and $M$-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the $H$-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the $M$-driven loop is re-entrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.Comment: 11 pages, 11 figure

Influence of Elastic Strains on the Adsorption Process in Porous Materials. An Experimental Approach

The experimental results presented in this paper show the influence of the elastic deformation of porous solids on the adsorption process. With p+-type porous silicon formed on highly boron doped (100) Si single crystal, we can make identical porous layers, either supported by or detached from the substrate. The pores are perpendicular to the substrate. The adsorption isotherms corresponding to these two layers are distinct. In the region preceding capillary condensation, the adsorbed amount is lower for the membrane than for the supported layer and the hysteresis loop is observed at higher pressure. We attribute this phenomenon to different elastic strains undergone by the two layers during the adsorption process. For the supported layer, the planes perpendicular to the substrate are constrained to have the same interatomic spacing as that of the substrate so that the elastic deformation is unilateral, at an atomic scale, and along the pore axis. When the substrate is removed, tridimensional deformations occur and the porous system can find a new configuration for the solid atoms which decreases the free energy of the system adsorbate-solid. This results in a decrease of the adsorbed amount and in an increase of the condensation pressure. The isotherms for the supported porous layers shift toward that of the membrane when the layer thickness is increased from 30 to 100 microns. This is due to the relaxation of the stress exerted by the substrate as a result of the breaking of Si-Si bonds at the interface between the substrate and the porous layer. The membrane is the relaxed state of the supported layer.Comment: Accepted in Langmui

The Ideal Conductor Limit

This paper compares two methods of statistical mechanics used to study a classical Coulomb system S near an ideal conductor C. The first method consists in neglecting the thermal fluctuations in the conductor C and constrains the electric potential to be constant on it. In the second method the conductor C is considered as a conducting Coulomb system the charge correlation length of which goes to zero. It has been noticed in the past, in particular cases, that the two methods yield the same results for the particle densities and correlations in S. It is shown that this is true in general for the quantities which depend only on the degrees of freedom of S, but that some other quantities, especially the electric potential correlations and the stress tensor, are different in the two approaches. In spite of this the two methods give the same electric forces exerted on S.Comment: 19 pages, plain TeX. Submited to J. Phys. A: Math. Ge

Critical behavior of a fluid in a disordered porous matrix: An Ornstein-Zernike approach

Using a liquid-state approach based on Ornstein-Zernike equations, we study the behavior of a fluid inside a porous disordered matrix near the liquid-gas critical point.The results obtained within various standard approximation schemes such as lowest-order $\gamma$-ordering and the mean-spherical approximation suggest that the critical behavior is closely related to that of the random-field Ising model (RFIM).Comment: 10 pages, revtex, to appear in Physical Review Letter

Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited

We revisit the model of a Brownian particle in a heat bath submitted to an actively controlled force proportional to the velocity that leads to thermal noise reduction (cold damping). We investigate the influence of the continuous feedback on the fluctuations of the total entropy production and show that the explicit expression of the detailed fluctuation theorem involves different dynamics and observables in the forward and backward processes. As an illustration, we study the analytically solvable case of a harmonic oscillator and calculate the characteristic function of the entropy production in a nonequilibrium steady state. We then determine the corresponding large deviation function which results from an unusual interplay between 'boundary' and 'bulk' contributions.Comment: 16 pages, 5 figures. References 9,10,13,14,15 added. A few changes in the text. Accepted for publication in J. Stat. Mec

Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior

We study the interplay between hysteresis and equilibrium behavior in capillary condensation of fluids in mesoporous disordered materials via a mean-field density functional theory of a disordered lattice-gas model. The approach reproduces all major features observed experimentally. We show that the simple van der Waals picture of metastability fails due to the appearance of a complex free-energy landscape with a large number of metastable states. In particular, hysteresis can occur both with and without an underlying equilibrium transition, thermodynamic consistency is not satisfied along the hysteresis loop, and out-of-equilibrium phase transitions are possible.Comment: 4 pages, 4 figure