In the immediate vicinity of the critical temperature (T$_c$) of a phase transition, there are fluctuations of the order parameter, which reside beyond the mean-field approximation. Such critical fluctuations usually occur in a very narrow temperatur
e window in contrast to Gaussian fluctuations. Here, we report on a study of specific heat in graphite subject to high magnetic field when all carriers are confined in the lowest Landau levels. The observation of a BCS-like specific heat jump in both temperature and field sweeps establishes that the phase transition discovered decades ago in graphite is of the second-order. The jump is preceded by a steady field-induced enhancement of the electronic specific heat. A modest (20 percent) reduction in the amplitude of the magnetic field (from 33 T to 27 T) leads to a threefold decrease of T$_c$ and a drastic widening of the specific heat anomaly, which acquires a tail spreading to two times T$_c$. We argue that the steady departure from the mean-field BCS behavior is the consequence of an exceptionally large Ginzburg number in this dilute metal, which grows steadily as the field lowers. Our fit of the critical fluctuations indicates that they belong to the $3DXY$ universality class, similar to the case of $^4$He superfluid transition.
Asymptotics deviation probabilities of the sum S n = X 1 + $times$ $times$ $times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated , in particular when X 1 is not exponentially integrab
le. For instance, A.V. Nagaev formulated exact asymptotics results for P(S n > x n) when X 1 has a semiexponential distribution (see, [16, 17]). In the same setting, the authors of [4] derived deviation results at logarithmic scale with shorter proofs relying on classical tools of large deviation theory and expliciting the rate function at the transition. In this paper, we exhibit the same asymptotic behaviour for triangular arrays of semiexponentially distributed random variables, no more supposed absolutely continuous.
Sensitivity indices are commonly used to quantity the relative inuence of any specic group of input variables on the output of a computer code. In this paper, we focus both on computer codes the output of which is a cumulative distribution function a
nd on stochastic computer codes. We propose a way to perform a global sensitivity analysis for these kinds of computer codes. In the rst setting, we dene two indices: the rst one is based on Wasserstein Fr{e}chet means while the second one is based on the Hoeding decomposition of the indicators of Wasserstein balls. Further, when dealing with the stochastic computer codes, we dene an ideal version of the stochastic computer code thats ts into the frame of the rst setting. Finally, we deduce a procedure to realize a second level global sensitivity analysis, namely when one is interested in the sensitivity related to the input distributions rather than in the sensitivity related to the inputs themselves. Several numerical studies are proposed as illustrations in the dierent settings.
Asymptotics deviation probabilities of the sum S n = X 1 + $times$ $times$ $times$ + X n of independent and identically distributed real-valued random variables have been extensively investigated, in particular when X 1 is not exponentially integrabl
e. For instance, A.V. Nagaev formulated exact asymptotics results for P(S n > x n) when x n > n 1/2 (see, [13, 14]). In this paper, we derive rough asymptotics results (at logarithmic scale) with shorter proofs relying on classical tools of large deviation theory and expliciting the rate function at the transition.
In this paper, we introduce new indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called Sobol indices and the Cram{e}r-von-Mises indices. Furthermore, we provi
de asymptotically Gaussian estimators of these indices based on U-statistics. Surprisingly, we prove the asymp-totic normality straightforwardly. Finally, we illustrate this new procedure on a toy model and on two real-data examples.
As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.
We consider the model of hashing with linear probing and we establish the moderate and large deviations for the total displacement in sparse tables. In this context, Weibull-like-tailed random variables appear. Deviations for sums of such heavy-taile
d random variables are studied in cite{Nagaev69-1,Nagaev69-2}. Here we adapt the proofs therein to deal with conditioned sums of such variables and solve the open question in cite{TFC12}. By the way, we establish the deviations of the total displacement in full tables, which can be derived from the deviations of empirical processes of i.i.d. random variables established in cite{Wu94}..
The magnetic penetration depth $lambda$ has been measured in MgCNi$_{3}$ single crystals using both a high precision Tunnel Diode Oscillator technique (TDO) and Hall probe magnetization (HPM). In striking contrast to previous measurements in powders,
$deltalambda$(T) deduced from TDO measurements increases exponentially at low temperature, clearly showing that the superconducting gap is fully open over the whole Fermi surface. An absolute value at zero temperature $lambda(0)=230 $nm is found from the lower critical field measured by HPM. We also discuss the observed difference of the superfluid density deduced from both techniques. A possible explanation could be due to a systematic decrease of the critical temperature at the sample surface.
We report on local magnetization, tunnel diode oscillators, and specific-heat measurements in a series of Ba(NixFe1-x)2As2 single crystals (0.26leqxleq0.74). We show that the London penetration depth lambda(T)=lambda(0)+Deltalambda(T) scales as lambd
a(0)propto1/Tc0.85$pm$0.2, Deltalambda(T)proptoT2.3$pm$0.3 (for T
A new calorimeter for measurements of the AC heat capacity and magnetocaloric effect of small samples in pulsed magnetic fields is discussed for the exploration of thermal and thermodynamic properties at temperatures down to 2 K. We tested the method
up to mu 0H = 50 Tesla, but it could be extended to higher fields. For these measurements we used carefully calibrated bare chip Cernoxtextregistered and RuO2 thermometers, and we present a comparison of their performance. The monotonic temperature and magnetic field dependences of the magneto resistance of RuO2 allow us to carry on precise thermometry with a precision as good as pm 1mK at T = 2 K. To test the performance of our calorimeter, AC heat capacity and magnetocaloric effect for the spin-dimer compound Sr3Cr2O8 and the triangular lattice antiferromagnet RbFe(MoO4)2 are presented.
