Self-Averaging, Distribution of Pseudo-Critical Temperatures and Finite Size Scaling in Critical Disordered Systems

The distributions $P(X)$ of singular thermodynamic quantities in an ensemble of quenched random samples of linear size $l$ at the critical point $T_c$ are studied by Monte Carlo in two models. Our results confirm predictions of Aharony and Harris based on Renormalization group considerations. For an Ashkin-Teller model with strong but irrelevant bond randomness we find that the relative squared width, $R_X$, of $P(X)$ is weakly self averaging. $R_X\sim l^{\alpha/\nu}$, where $\alpha$ is the specific heat exponent and $\nu$ is the correlation length exponent of the pure model fixed point governing the transition. For the site dilute Ising model on a cubic lattice, known to be governed by a random fixed point, we find that $R_X$ tends to a universal constant independent of the amount of dilution (no self averaging). However this constant is different for canonical and grand canonical disorder. We study the distribution of the pseudo-critical temperatures $T_c(i,l)$ of the ensemble defined as the temperatures of the maximum susceptibility of each sample. We find that its variance scales as $(\delta T_c(l))^2 \sim l^{-2/\nu}$ and NOT as $\sim l^{-d}. We find that$R_\chi$is reduced by a factor of$\sim 70$with respect to$R_\chi (T_c)$by measuring$\chi$of each sample at$T_c(i,l)$. We analyze correlations between the magnetization at criticality$m_i(T_c,l)$and the pseudo-critical temperature$T_c(i,l)$in terms of a sample independent finite size scaling function of a sample dependent reduced temperature$(T-T_c(i,l))/T_c$. This function is found to be universal and to behave similarly to pure systems.Comment: 31 pages, 17 figures, submitted to Phys. Rev.

Biomarkers of Multiple Sclerosis

The search for an ideal multiple sclerosis biomarker with good diagnostic value, prognostic reference and an impact on clinical outcome has yet to be realized and is still ongoing. The aim of this review is to establish an overview of the frequent biomarkers for multiple sclerosis that exist to date. The review summarizes the results obtained from electronic databases, as well as thorough manual searches. In this review the sources and methods of biomarkers extraction are described; in addition to the description of each biomarker, determination of the prognostic, diagnostic, disease monitoring and treatment response values besides clinical impact they might possess. We divided the biomarkers into three categories according to the achievement method: laboratory markers, genetic-immunogenetic markers and imaging markers. We have found two biomarkers at the time being considered the gold standard for MS diagnostics. Unfortunately, there does not exist a single solitary marker being able to present reliable diagnostic value, prognostic value, high sensitivity and specificity as well as clinical impact. We need more studies to find the best biomarker for MS.publishersversionPeer reviewe