There is a certain consensus that the very fast growth of the relaxation time $τ$ occurring in glass-forming liquids on lowering the temperature must be due to the thermally activated rearrangement of correlated regions of growing size. Even though measuring the size of these regions has defied scientists for a while, there is indeed recent evidence of a growing correlation length $ξ$ in glass-formers. If we use Arrhenius law and make the mild assumption that the free-energy barrier to rearrangement scales as some power $ψ$ of the size of the correlated regions, we obtain a relationship between time and length, $T\logτ\sim ξ^ψ$. According to both the Adam-Gibbs and the Random First Order theory the correlation length grows as $ξ\sim (T-T_k)^{-1/(d-θ)}$, even though the two theories disagree on the value of $θ$. Therefore, the super-Arrhenius growth of the relaxation time with the temperature is regulated by the two exponents $ψ$ and $θ$ through the relationship $T\logτ\sim (T-T_k)^{-ψ/(d-θ)}$. Despite a few theoretical speculations, up to now there has been no experimental determination of these two exponents. Here we measure them numerically in a model glass-former, finding $ψ=1$ and $θ=2$. Surprisingly, even though the values we found disagree with most previous theoretical suggestions, they give back the well-known VFT law for the relaxation time, $T\logτ\sim (T-T_k)^{-1}$.
Low energy excitations in a long prism geometry: testing the lower critical dimension of the Ising spin glass
Istituto per le Applicazioni del Calcolo, CNR（意大利国家研究委员会计算应用研究所）；Universidad Complutense de Madrid（马德里康普顿斯大学）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新学院）；Dipartimento di Fisica, Sapienza Università di Roma（罗马大学物理系）；CNR-Nanotec, Rome Unit（意大利国家研究委员会纳米技术研究所罗马分部）；INFN, Sezione di Roma（罗马国立核物理研究所）
