Slow dynamics for the dilute Ising model in the phase coexistence region

In this paper we consider the Glauber dynamics for a disordered ferromagnetic Ising model, in the region of phase coexistence. It was conjectured several decades ago that the spin autocorrelation decays as a negative power of time [Huse and Fisher, Phys. Rev. B, 1987]. We confirm this behavior by establishing a corresponding lower bound in any dimensions $d \geqslant 2$, together with an upper bound when $d=2$. Our approach is deeply connected to the Wulff construction for the dilute Ising model. We consider initial phase profiles with a reduced surface tension on their boundary and prove that, under mild conditions, those profiles are separated from the (equilibrium) pure plus phase by an energy barrier.Comment: 44 pages, 6 figure

Metastability in the dilute Ising model

Consider Glauber dynamics for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. In this paper we show that even an arbitrarily small dilution can dramatically reduce the relaxation time. This is because of a catalyst effect---rare regions of high dilution speed up the transition from minus phase to plus phase.Comment: 49 page

Thermodynamic versus Topological Phase Transitions: Cusp in the Kert\'esz Line

We present a study of phase transitions of the Curie--Weiss Potts model at (inverse) temperature $\beta$, in presence of an external field $h$. Both thermodynamic and topological aspects of these transitions are considered. For the first aspect we complement previous results and give an explicit equation of the thermodynamic transition line in the $\beta$--$h$ plane as well as the magnitude of the jump of the magnetization (for $q \geqslant 3)$. The signature of the latter aspect is characterized here by the presence or not of a giant component in the clusters of a Fortuin--Kasteleyn type representation of the model. We give the equation of the Kert\'esz line separating (in the $\beta$--$h$ plane) the two behaviours. As a result, we get that this line exhibits, as soon as $q \geqslant 3$, a very interesting cusp where it separates from the thermodynamic transition line

Strengths and Weaknesses of the Vascular Apathy Hypothesis:A Narrative Review

The vascular apathy hypothesis states that cerebral small vessel disease (CSVD) can cause apathy, even when no other symptoms of CSVD are present. In order to examine this hypothesis, the objectives of this narrative review are to evaluate the evidence for a pathophysiological mechanism linking CSVD to apathy and to examine whether CSVD can be a sole cause of apathy. The nature of the CSVD-apathy relationship was evaluated using the Bradford Hill criteria as a method for research on the distinction between association and causation. Pathological, neuroimaging, and behavioral studies show that CSVD can cause lesions in the reward network, which causes an apathy syndrome. Studies in healthy older individuals, stroke patients and cognitively impaired persons consistently show an association between CSVD markers and apathy, although studies in older persons suffering from depression are inconclusive. A biological gradient is confirmed, as well as a temporal relationship, although the evidence for the latter is still weak. The specificity of this causal relationship is low given there often are other contributing factors in CSVD patients with apathy, particularly depression and cognitive deterioration. Differentiating between vascular apathy and other apathy syndromes on the basis of clinical features is not yet possible, while in-depth knowledge about differences in the prognosis and efficacy of treatment options for apathy caused by CSVD and other apathy syndromes is lacking. Since we cannot differentiate between etiologically different apathy syndromes as yet, it is premature to use the term vascular apathy which would suggest a distinct clinical apathy syndrome

Surface tension in the dilute Ising model. The Wulff construction

We study the surface tension and the phenomenon of phase coexistence for the Ising model on \mathbbm{Z}^d ($d \geqslant 2$) with ferromagnetic but random couplings. We prove the convergence in probability (with respect to random couplings) of surface tension and analyze its large deviations : upper deviations occur at volume order while lower deviations occur at surface order. We study the asymptotics of surface tension at low temperatures and relate the quenched value $\tau^q$ of surface tension to maximal flows (first passage times if $d = 2$). For a broad class of distributions of the couplings we show that the inequality $\tau^a \leqslant \tau^q$ -- where $\tau^a$ is the surface tension under the averaged Gibbs measure -- is strict at low temperatures. We also describe the phenomenon of phase coexistence in the dilute Ising model and discuss some of the consequences of the media randomness. All of our results hold as well for the dilute Potts and random cluster models

Stretched Polymers in Random Environment

We survey recent results and open questions on the ballistic phase of stretched polymers in both annealed and quenched random environments.Comment: Dedicated to Erwin Bolthausen on the occasion of his 65th birthda

Projecting picosecond lattice dynamics through x-ray topography

A method for time-resolved x-ray diffraction studies has been demonstrated. As a test case, coherent acoustic phonon propagation into crystalline InSb is observed using a laser plasma x-ray source. An extended x-ray topogram of the semiconductor's surface was projected onto a high spatial resolution x-ray detector and acoustic phonons were excited by rapidly heating the crystal's surface with a femtosecond laser pulse. A correlation between the spatial position on the x-ray detector and the time of arrival of the laser pulse was encoded into the experimental geometry by tilting the incident laser pulse with an optical grating. This approach enabled a temporal window of 200 ps to be sampled in a single topogram, thereby negating the disadvantages of pulse-to-pulse fluctuations in the intensity and spectrum of the laser-plasma source. (C) 2002 American Institute of Physics