Application of p-adic analysis to models of spontaneous breaking of the replica symmetry

Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page

Imaging the environmental ultraviolet

A technique has been developed to visually represent measured environmental ultraviolet radiation using a digital photograph and measurements of the UV and visible light intensity. The method involves the use of a personal pocket UV meter, an optional lux meter and a simple image processing technique to present visual images that are weighted to the ambient ultraviolet, providing images that highlight regions of high ultraviolet intensity that can be compared with a visible photograph. The technique described, provides a method students can follow to better develop an understanding of the potentially harmful ultraviolet irradiance with respect to visible daylight, indicating that the ambient ultraviolet and visible environment are not directly related, with ultraviolet intensity being dependent on many different factors and not the visual brightness of the location alone

Assessment of ultraviolet radiation exposures in photobiological experiments

The interfering effect of ultraviolet (UV) radiation on the natural function of biological processes is wavelength specific and the UV spectrum must be weighted with the action spectrum for the process. The UV spectral irradiance may be measured with calibrated spectroradiometers. Alternatively, the biologically effective UV may be measured with broadband devices. This paper reviews the techniques for assessing biologically effective exposures in photobiological experiments. UV meters, such as the Robertson-Berger (RB) meter, or passive dosimeters, such as polysulphone, that possess a spectral response approximating the human erythemal response can be used to estimate erythemally effective exposure or actinic exposure due to solar UV. The sensitivity of the RB meter is about 0.56 uW cm-2 and polysulphone can record an exposure of about 2mJ cm-2. For photobiological processes other than erythema these devices are not suitable to determine the exposure. In terms of these applications, a spectrum evaluator consisting of four different types of dosimeter material can be employed to evaluate the UV spectrum of the source. This method can be useful both for solar UV studies and research with UV lamps that possess radiation wavelengths shorter than 295nm. The device can be used to measure exposures where the actinic and erythemal action spectra differ significantly. It can also be used to assess exposure due to low levels of UV (about 0.01uW cm-2) caused by radiation filtered through glasses or plastic

Effect of cloud on UVA and exposure to humans

The daily autumn and winter UVA exposures and 6-minute UVA irradiance data for a Southern Hemisphere, subtropical site (Toowoomba, Australia, 27.6 S, 151.9 E) are presented. This data is used to quantify the effect of cloud on UVA using an integrated sky-camera and radiation system. Additionally, an estimate of the effect of enhanced UVA exposure on humans is made. The measurement system consisted of broadband visible-infrared and UVA sensors together with a sun tracking, wide-angle video camera. The mean daily June exposure was found to be 409 kJm-2. Under the constraints of the uncertainty of both the UVA measurement system and clear-sky model, one case of enhanced UVA irradiance was found. Three cases of cloud enhancement of daily UVA exposure, approaching clear-sky levels, were also determined using a calculated clear-sky envelope. It was also determined that for a fulltime outdoor worker, the additional UVA exposure could approach approximately that of one third of a full winter's day. For indoor workers with an outside lunch break of noon to 1 pm, the additional UVA exposure was on average 6.9 kJm-2 over three cloud enhanced days. To the authors' knowledge this is the first paper to present some evidence of cloud enhanced UVA human exposure

Finite-size scaling study of the d=4 site-diluted Ising

We study the four dimensional site-diluted Ising model using finite-size scaling techniques. We explore the whole parameter space (density-coupling) in order to determine the Universality Class of the transition line. Our data are compatible with Mean Field behavior plus logarithmic corrections.Comment: Contribution to LATTICE 9

Continuous RSB mean-field solution of the Potts glass

We investigate the p-state mean-field model of the Potts glass ($2\le p \le 4$) below the continuous phase transition to a glassy phase. We find that apart from a solution with a first hierarchical level of replica-symmetry breaking (1RSB), locally stable close to the transition point, there is a continuous full replica-symmetry breaking (FRSB) solution. The latter is marginally stable and has a higher free energy than the former. We argue that the true equilibrium is reached only by FRSB, being globally thermodynamically homogeneous, whereas 1RSB is only locally homogeneous.Comment: REVTeX4.1, 4 pages, 1 figur

Replica Symmetry Breaking and the Renormalization Group Theory of the Weakly Disordered Ferromagnet

We study the critical properties of the weakly disordered $p$-component ferromagnet in terms of the renormalization group (RG) theory generalized to take into account the replica symmetry breaking (RSB) effects coming from the multiple local minima solutions of the mean-field equations. It is shown that for $p < 4$ the traditional RG flows at dimensions $D=4-\epsilon$, which are usually considered as describing the disorder-induced universal critical behavior, are unstable with respect to the RSB potentials as found in spin glasses. It is demonstrated that for a general type of the Parisi RSB structures there exists no stable fixed points, and the RG flows lead to the {\it strong coupling regime} at the finite scale $R_{*} \sim \exp(1/u)$, where $u$ is the small parameter describing the disorder. The physical concequences of the obtained RG solutions are discussed. In particular, we argue, that discovered RSB strong coupling phenomena indicate on the onset of a new spin glass type critical behaviour in the temperature interval $\tau < \tau_{*} \sim \exp(-1/u)$ near $T_{c}$. Possible relevance of the considered RSB effects for the Griffith phase is also discussed.Comment: 32 pages, Late

Temperature chaos in 3D Ising Spin Glasses is driven by rare events

Temperature chaos has often been reported in literature as a rare-event driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a large-deviations functional that allows to discuss the size dependencies. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.Comment: 5 pages, 5 figure

Temperature chaos is a non-local effect

Temperature chaos plays a role in important effects, like for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precise the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.Comment: 15 pages, 8 figures. Version accepted for publication in JSTA

Langevin Simulation of the Chirally Decomposed Sine-Gordon Model

A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing with these models, alternative computational strategies have been proposed along the years. The Langevin technique, in particular, is known to be frequently plagued with difficulties such as strong numerical instabilities or subtle ergodic behavior. Regarding the chirally decomposed version of the sine-Gordon model as a prototypical case for the failure of the Langevin approach, we devise a truncation prescription in the stochastic differential equations which yields numerical stability and is assumed not to spoil the Berezinskii-Kosterlitz-Thouless transition. This conjecture is supported by a finite size scaling analysis, whereby a massive phase ending at a line of critical points is clearly observed for the truncated stochastic model.Comment: 6 pages, 4 figure