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Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-μm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

Recently, Auffinger, Ben Arous and Černý initiated the study of critical points of the Hamiltonian in the spherical pure p-spin spin glass model, and established connections between those and several notions from the physics literature. Denoting the number of critical values less than Nu by CrtN(u), they computed the asymptotics of $\\frac{1}{\\mathrm{N}} \\ \\mathrm{log}\\left(\\mathrm{\\mathbb{E}}\\mathrm{C}\\mathrm{r}{\\mathrm{t}}_{\\mathrm{N}}\\right(\\mathrm{u}\\left)\\right)$, as N, the dimension of the sphere, goes to ∞. We compute the asymptotics of the corresponding second moment and show that, for p ≥ 3 and sufficiently negative u, it matches the first moment: 𝔼{(CrtN(u))2}/(𝔼{CrtN(u)})2 → 1. As an immediate consequence we obtain that CrtN(u)/𝔼{CrtN(u)} → 1, in L2, and thus in probability. For any u for which 𝔼CrtN(u) does not tend to 0 we prove that the moments match on an exponential scale.

Bond critical points (BCPs) in the quantum theory of atoms in molecules (QTAIM) are shown to be a consequence of the molecular topology, symmetry, and the Poincaré-Hopf relationship, which defines the numbers of critical points of different types in a scalar field. BCPs can be induced by a polarizing field or by addition of a single non-bonded atom to a molecule. BCPs and their associated bond paths are therefore suggested not to be a suitable means of identifying chemical bonds, or even attractive intermolecular interactions. Graphical abstract Bond-critical points in QTAIM and weak interactionsᅟ

Let pnp_n be a random, degree nn polynomial whose roots are chosen independently according to the probability measure μ\\mu on the complex plane. For a deterministic point ξ\\xi lying outside the support of μ\\mu, we show that almost surely the polynomial qn(z):=pn(z)(z−ξ)q_n(z):=p_n(z)(z - \\xi ) has a critical point at distance O(1/n)O(1/n) from ξ\\xi. In other words, conditioning the random polynomials pnp_n to have a root at ξ\\xi almost surely forces a critical point near ξ\\xi. More generally, we prove an analogous result for the critical points of qn(z):=pn(z)(z−ξ1)⋯(z−ξk)q_n(z):=p_n(z)(z - \\xi _1) \\cdots (z - \\xi _k), where ξ1,…,ξk\\xi _1, \\ldots , \\xi _k are deterministic. In addition, when k=o(n)k=o(n), we show that the empirical distribution constructed from the critical points of qnq_n converges to μ\\mu in probability as the degree tends to infinity, extending a recent result of Kabluchko [Proc. Amer. Math. Soc. 143 (2015), no. 2, 695–702].

We developed the RexPoN force field for water based entirely on quantum mechanics. It predicts the properties of water extremely accurately, with T melt = 273.3 K (273.15 K) and properties at 298 K: ΔHvap = 10.36 kcal/mol (10.52), density = 0.9965 g/cm³ (0.9965), entropy = 68.4 J/mol/K (69.9), and dielectric constant = 76.1 (78.4), where experimental values are in parentheses. Upon heating from 0.0 K (ice) to 273.0 K (still ice), the average number of strong hydrogen bonds (SHBs, rOO ≤ 2.93 Å) decreases from 4.0 to 3.3, but upon melting at 273.5 K, the number of SHBs drops suddenly to 2.3, decreasing slowly to 2.1 at 298 K and 1.6 at 400 K. The lifetime of the SHBs is 90.3 fs at 298 K, increasing monotonically for lower temperature. These SHBs connect to form multibranched polymer chains (151 H₂O per chain at 298 K), where branch points have 3 SHBs and termination points have 1 SHB. This dynamic fluctuating branched polymer view of water provides a dramatically modified paradigm for understanding the properties of water. It may explain the 20-nm angular correlation lengths at 298 K and the critical point at 227 K in supercooled water. Indeed, the 15% jump in the SHB lifetime at 227 K suggests that the supercooled critical point may correspond to a phase transition temperature of the dynamic polymer structure. This paradigm for water could have a significant impact on the properties for protein, DNA, and other materials in aqueous media.

When a symmetry-breaking phase of matter is suppressed to a quantum critical point (QCP) at absolute zero, quantum-mechanical fluctuations proliferate. Such fluctuations can lead to unconventional superconductivity, as evidenced by the superconducting domes often found near magnetic QCPs in correlated materials. Experimentally, however, it remains much less clear whether the superconductivity can be promoted around QCPs of the electronic nematic phase, characterized by rotational symmetry breaking. Here, we demonstrate from systematic elastoresistivity measurements that nonmagnetic FeSe1−x Teₓ exhibits an electronic nematic QCP showing diverging nematic susceptibility. This finding establishes two nematic QCPs in FeSe-based superconductors with contrasting accompanying phase diagrams. In FeSe1−x Teₓ, a superconducting dome is centered at the QCP, whereas FeSe1−x Sₓ shows no QCP-associated enhancement of superconductivity. We find that this difference is related to the relative strength of nematic and spin fluctuations. Our results in FeSe1−x Teₓ present the unprecedented case in support of the superconducting dome being associated with the QCP of pure electronic nematic order, which does not intertwine with any other long-range orders.

An exciton is an electron–hole pair bound by attractive Coulomb interaction. Short-lived excitons have been detected by a variety of experimental probes in numerous contexts. An excitonic insulator, a collective state of such excitons, has been more elusive. Here, thanks to Nernst measurements in pulsed magnetic fields, we show that in graphite there is a critical temperature (T = 9.2 K) and a critical magnetic field (B = 47 T) for Bose–Einstein condensation of excitons. At this critical field, hole and electron Landau subbands simultaneously cross the Fermi level and allow exciton formation. By quantifying the effective mass and the spatial separation of the excitons in the basal plane, we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature. This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.

Spinless fermions on a honeycomb lattice provide a minimal realization of lattice Dirac fermions. Repulsive interactions between nearest neighbors drive a quantum phase transition from a Dirac semimetal to a charge-density-wave state through a fermionic quantum critical point, where the coupling of the Ising order parameter to the Dirac fermions at low energy drastically affects the quantum critical behavior. Encouraged by a recent discovery (Huffman and Chandrasekharan 2014 Phys. Rev. B 89 111101) of the absence of the fermion sign problem in this model, we study the fermionic quantum critical point using the continuous-time quantum Monte Carlo method with a worm-sampling technique. We estimate the transition point with the critical exponents and . Compatible results for the transition point are also obtained with infinite projected entangled-pair states.

We investigate, for two water models displaying a liquid-liquid critical point, the relation between changes in dynamic and ther-modynamic anomalies arising from the presence of the liquid-liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima$C_{P}^{max}$(\"Widom line\") emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid-liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between$C_{P}^{max}$and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid-liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.

The engineering behaviour of rock is strongly associated with the anisotropy, which exists at different scales for construction safety and evaluation of rock properties. It is also well known that the anisotropy of the drilling mechanical characteristics in the rock cutting process has an essential effect on the drilling efficiency and cost. For this purpose, an effort was made to characterize the anisotropy of the drilling mechanical characteristics of rocks in the rock drilling process. The drilling strength and specific energy at the cutting point are considered to characterize the drilling process in three different directions according to the drilling response model. A drilling characteristic-based index is proposed to evaluate the anisotropy of rock. Drilling tests were conducted in three directions for six types of rock to study the anisotropy variation along the borehole depth. The anisotropy evolution result along the borehole suggested that this critical point is identified as the cutting point, dividing the drilling process into two stages of cutting and frictional contact. The cutting point also shows anisotropic features. The anisotropic ranking of tested rocks was obtained. Based on how the drilling parameters depend on the unconfined compressive strength, the reliability of the proposed anisotropy index is examined by comparison with the strength anisotropy index. The comparative result demonstrates that the proposed method can provide a reliable determination for rock anisotropy by using the drilling strength. The work performed in this paper provides a very useful approach for evaluating the anisotropy of rock and provides a good understanding of the drilling mechanical characteristics in rock drilling.HighlightsThe anisotropy of the drilling mechanical characteristics of rocks is characterized in the rock drilling process.The drilling strength and specific energy at the cutting point are considered to characterize the drilling process in three different directions.A drilling characteristic-based index is proposed to evaluate the anisotropy of rock.Drilling tests are conducted in three directions for six types of rock to study the anisotropy variation along the borehole depth.