Speaker
Description
The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently for the three-dimensional Ising model, the calculation of the probability distribution function (PDF) of the total spin: $P(L^{-d}\int d^{d}x~\phi(x)=s)$ at criticality has been performed with the functional renormalization group. It has been shown that there exists an entire family of universal PDFs $P_{\zeta}(s)$ parameterized by $\zeta=\lim_{L,\xi_\infty\rightarrow\infty}L/\xi_\infty$ which is the ratio of the system size $L$ to the bulk correlation length $\xi_{\infty}$ with both $L,\xi_{\infty}\to\infty$. Using the $\epsilon=4-d$ expansion scheme in perturbation theory, we compute in three dimensions the whole family of $P_{\zeta}(s)$ up to two-loop order. I will finally show that in $d\geq 4$, even though the infrared-fluctuations are Gaussian--these universal PDFs are not, thereby showing why triviality doesn't mean Gaussianity.
| Affiliation | LPTMC, Sorbonne Université |
|---|---|
| Link to paper | https://doi.org/10.1103/PhysRevE.111.034128 |
| Career status | PhD student |