Three-dimensional critical behavior with 2D, 1D, and 0D dimensionality crossover: surface and edge specific heats

Surface-Dominated Finite-Size Effects in Nanoconfined Superfluid Helium

Superfluid ^{4}He (He II) is a widely studied model system for exploring finite-size effects in strongly confined geometries. Here, we study He II confined in millimeter-scale channels of 25 and 50 nm height at high pressures using a nanofluidic Helmholtz resonator. We find that the superfluid density is measurably suppressed in the confined geometry from the transition temperature down to 0.6 K. Importantly, this suppression can be accounted for by rotonlike thermal excitations with an energy gap of 5 K. We show that the surface-bound excitations lead to the previously unexplained lack of finite-size scaling of suppression of the superfluid density.

A review of giant correlation-length effects via proximity and weak-links coupling in a critical system: 4He near the superfluid transition

We review measurements of ⁴He near the superfluid transition in arrangements whereby an array of weak links couple relatively larger, more bulk-like ⁴He regions. In contrast to experiments which focus on the dependence of the superflow on the chemical potential difference across the links, these studies focus on the specific heat of both the weak links and that of the larger coupled regions, as well as the behavior of the superfluid fraction within the weak links. The data show unexpected results which reflect a very long range coupling as well as modification of the weak link itself due to the proximity to bulk-like helium. One finds that while the three-dimensional correlation length [Formula: see text], where [Formula: see text], is involved in these long-range effects, the distance over which these can be seen is of the order of 100 to 1000 times [Formula: see text]. These results call into question our understanding of the meaning of the correlation length at a critical point as the 'range' over which information can propagate. These studies are the first to measure the thermodynamic properties of weak links for a critical system where fluctuations are important. They differ in essential ways with expectations from mean-field considerations. We compare results with other ⁴He measurements, with superconductors and the theoretical calculations of the Ising model.

Criticality in alternating layered Ising models. I. Effects of connectivity and proximity

The specific heats of exactly solvable alternating layered planar Ising models with strips of width m_{1} lattice spacings and "strong" couplings J_{1} sandwiched between strips of width m_{2} and "weak" coupling J_{2}, have been studied numerically to investigate the effects of connectivity and proximity. We find that the enhancements of the specific heats of the strong layers and of the overall or "bulk" critical temperature T_{c}(J_{1},J_{2};m_{1},m_{2}) arising from the collective effects reflect the observations of Gasparini and co-workers in experiments on confined superfluid helium. Explicitly, we demonstrate that finite-size scaling holds in the vicinity of the upper limiting critical point T_{1c} (∝J_{1}/k_{B}) and close to the corresponding lower critical limit T_{2c} (∝J_{2}/k_{B}) when m_{1} and m_{2} increase. However, the residual enhancement, defined via appropriate subtractions of leading contributions from the total specific heat, is dominated (away from T_{1c} and T_{2c}) by a decay factor 1/(m_{1}+m_{2}) arising from the seams (or boundaries) separating the strips; close to T_{1c} and T_{2c} the decay is slower by a factor lnm_{1} and lnm_{2}, respectively.