Corrections to scaling and surface specific heat of confined helium

Self Cite

We report measurements of the specific heat of thick helium films to test scaling predictions near the superfluid transition, T l . These films, bounded by two silicon wafers, range in thickness from 0.107 to 0.692 mm. The specific heat of the films is suppressed relative to that of bulk helium, and the difference of the data from bulk helium scales well with the exponent of the correlation length. We propose an empirical scaling function which fits the data well for T . T l , and yields the surface specific heat. We also compare the data with various theoretical calculations and experiments. We find that the calculations underestimate the effect of confinement. [S0031-9007(97)

Section: Sarabjit Mehta and Francis M Gasparinisupporting

confidence: 45%

Section: Sarabjit Mehta and Francis M Gasparinimentioning

confidence: 99%

Specific Heat and Scaling of4HeConfined in a Planar Geometry

Mehta

Gasparini

1997

Self Cite

“…18,20 We find that our present data for T c are not precise enough to address the points raised in Refs. 18 and 20 .…”

mentioning

confidence: 50%

Universality of the Kosterlitz-Thouless Transition inHe4Films as a Function of Thickness

Finotello

Gasparini

1985

We report new measurements of thermal transport in 4 He films near the superfluid transition. We have done this to check on the universality of this transition as a function of thickness or T c between 1.37 and 1.88 K. Results from this study show for the first time a thickness or T c dependence of the two characteristic parameters for the thermal conduction, the ratio of diffusion constant to vortex core radius, D/a 2 , and the nonuniversal constant b. We suggest that the increase of b with film thickness is related to the bulk correlation length. PACS numbers: 64.70.-p, 67.40.pm, 67.70. + nThe superfluid transition in 4 He films has been studied extensively as one of the realizations of a twodimensional (2D) x-y system. Various predictions coming from the Kosterlitz-Thouless theory 1 of such a transition have been verified via measurements of the superfluid density, 2,3 thermal transport, 4 " 7 and persistent currents. 8 The transition is in the same universality class as, for instance, 2D melting, the superconducting transition in thin films, and some transitions in liquid crystals. It is thus of considerable theoretical and experimental interest. There are still, however, several aspects of the superfluid transition which merit further attention. Among these is the question of how this transition is modified when one deals with helium films substantially thicker than a few monolayers. One expects that as long as one is in a temperature region where the 3D correlation length would tend to be larger than the film thickness, then the 2D behavior should be manifest. It is clear, however, that aspects of this behavior must be modified in thick films, if for no other reason but the fact that the critical behavior is relegated to a progressively smaller region in temperature as the film's T c approaches the bulk 7\. We report in this Letter a study of thermal transport to look at this behavior. Our work can be viewed from the perspective of finite-size scaling and dimensionality crossover 9 but, perhaps more importantly, it should be viewed as a universality study of the KosterlitzThouless transition. This is analogous to the study of the critical behavior at the 3D superfluid transition along the A line on the pressure or 3 He-concentration plane. 10

“…Our present calculation does not yet explain the detailed L dependence of the height of the specific-heat maximum. 5 This may be due to the multimode problem 11 that one encounters in the crossover to the bulk behavior below 7\.…”

Section: F-[r-t C (L)]/t C (°O) Rather Than On T =*[T-t C (Oo)]/t C (mentioning

confidence: 98%

Possible Resolution of the Finite-Size Scaling Problem inHe4

Huhn

Dohm

1988

We offer an explanation of the long-standing discrepancy between finite-size scaling theory and the observed temperature shift 7\ -T m of the specific-heat maximum in confined 4 He. On the basis of a renormalization-group calculation using Dirichlet boundary conditions we argue that a new sizedependent scaling variable should be employed. The theory agrees with the data in the regime 7\ ^ T m without an adjustment of parameters and explains the gradual onset of finite-size effects far from 7\.PACS numbers: 67.40. Kh, 05.70.Jk, 64.60.Fr Since the early formulation of a phenomenological finite-size scaling theory of critical phenomena 1 there have been numerous theoretical studies and computer simulations on this subject. 2 Among the very few attempts to verify this theory by experiments in real systems there exists only one set of data at the required level of accuracy: the measurements of the critical specific heat and superfluid density in confined 4 He by Gasparini and co-workers. 3,4 It has therefore been a severe disappointment that just these data appear to contradict the scaling theory.The purpose of this Letter is to present detailed arguments and quantitative results that point towards a natural explanation of this long-standing problem. Our reasoning will be based entirely on the conventional Landau-Ginzburg-Wilson Hamiltonian for the n-component order parameter #(x) (n = 2 for 4 He),without accepting unusually large 5 correction-to-scaling amplitudes or invoking 6 surface fractal dimensionalities. Our new point is to incorporate fairly realistic (Dirichlet) boundary conditions (vanishing order parameter at the walls) in a quantitative renormalization-group calculation. No adjustment of nonuniversal amplitudes or couplings will be necessary because they are known from bulk theory 7 and independent bulk data. 8 Specifically, we shall discuss the heat capacity C of (x)~2 d/2 4 He confined in a geometry of size L. Our attention will be focused not only on the temperature shift 3 7\ -T m (L) of the specific-heat maximum and on the rounding temperature 1,2 T*(L), but also on a detailed comparison of the predicted T and L dependence of C(7\L) with the data in the regime T>T m . We shall show that Dirichlet boundary conditions (Dbc) have an unexpectedly large effect on these quantities. In particular, the conventional power law, 1 ' 2 T x -T m (L)~~L(2)where the bulk-correlation-length exponent is v -0.67, and should be replaced bywhere T C (L) < 7\ is an intrinsic reference temperature, the introduction of which suggests itself in the analysis. Furthermore, we find a gradual onset of finite-size effects far from 7\, which explains why previous results 3 concerning T*(L) were inconclusive. In order to substantiate these points it is necessary to describe our calculation in some detail. We have generalized the approach of Refs. 9 and 10 to the case of a cube with Dbc in d directions and periodic boundary conditions (pbc) in d -d directions. For simplicity we first consider d=d and AZ = 1. This case has been d...