Critical Point Pc Research Articles

Percolation in negative field and lattice animals.

We study in detail percolation in a negative ‘‘ghost’’ field, and show that the percolation model crosses over, in the presence of a negative field h, to the lattice-animal model, as predicted by the field theory. This was done by exact solutions in one dimension and on a Cayley tree, and series expansions in general dimension. We confirm the scaling picture near the percolation threshold, and study the extended scaling ansatz for all values of h in terms of the nonlinear scaling field gh. Estimates for gh are obtained as a function of h in all dimensions. We also show how information on percolation clusters in all concentrations up to the percolation threshold may be extracted by studying the critical behavior of the generalized susceptibilities χk(p,h) near their critical point pc(h) as a function of h, and obtain data on the cluster distribution function and on the ratio of perimeter bonds to cluster bonds, for large clusters for all 0≤p≤pc. The crossover function is studied in one dimension, mean-field theory and the e expansion.

Study of phase stability of β-(BEDT-TTF)2I3 by differential thermal analysis

We report a study of the pressure-temperature phase diagram of β-di[bis(ethyleneditio)tetrathiafulvalene] triiodide, β-(BEDT-TTF) 2I3, by a differential thermal analysis technique. We show that the nature of the state of the compound at low temperature depends on how cooling is achieved. A critical point (Pc ~ 345 bar, Tc ~ 150 K) plays a crucial role in this cooling process. The β- H phase displaying superconductivity at 8.1 K at ambient pressure is obtained by a clockwise pressure-temperature cycling around the critical point. We also show that an anticlockwise P — T cycling with P < Pc allows the stabilization of the low T c superconducting phase (β-L) at low temperature, very likely the phase displaying an incommensurate lattice distortion. The limit of stability of both β- Land β-H phases in the P — T diagram has been determined. The properties of metastability of the various phases of β-(BEDT-TTF)2I3 can be understood in terms of a Landau expansion of the free-energy with the appropriate pressure and temperature dependence of the second and fourth order terms of the expansion.

On the critical behavior of the surface tension in a random surface model

Abstract We examine the continuity of the surface tension α(p), at the critical point Pc, for the surfaces formed in the random plaquette model on Z3 - of independent plaquettes with density p. It is shown that α(p)⩽| In p|P ∞ 2 (1−p), and α(p)⩽| In p|P ∞ , 1 2 (1−p), where P ∞ (q) is the percolation probability in the dual bond percolation model - of independently occupied bonds with qand P ∞, 1 2 (q) is the percolation probability in the semi-infinite system. Under natural assumptions on the bond-percolation transition, these results strongly indicate that the surface tension vanishes continuously as p↑pc.

A majority-rule model : real-space renormalization-group solution and finite size scaling

Through a simple majority-rule a statistical geometrical d-dimensional model (d can even be a fractal dimensionality) is formulated which presents a continuous phase transition as a function of a certain independent occupancy probability p. Both critical point pc and « correlation length » exponent ν are exactly calculated through real-space renormalization-group (with linear scaling factor b). The well-known finite size scaling hypothesis ν(b) - ν ∝ 1/ln b (in the limit b → oo) is analytically exhibited. A more rapidly convergent finite size extrapolation procedure is presented.

The thermal conductivity of liquid and gaseous ammonia, and its anomalous behaviour in the vicinity of the critical point

The thermal conductivity of liquid and gaseous ammonia has been determined between 20° and 177°C and at pressures from 1 to 500 atm using a vertical, co-axial cylinder apparatus. Measurements in the vicinity of the critical point ( pc c = 111.5 atm, t c = 132.4° C) have been carried out with special care along the reduced isotherms, 1.016 and 1.061. An anomalous increase of thermal conductivity in this regime has been found, similar to that for carbon dioxide previously reported by two other observers. A tentative explanation of this phenomenon, based on transport of energy by clusters of molecules, is given. Experimental results for the liquid-like fluid state, both below and above the critical temperature, have been correlated by a quadratic equation between density and thermal conductivity. With the aid of this equation, values have been computed for conditions outside those of this study, and the table containing the smoothed, experimentally verified figures at even increments of pressure and temperature has been complemented by computed values ranging up to 1000 atm and 480°K. Computed values are also presented in tabular form for the technically important temperature range from room temperature to the normal fusion point (195.5°K). To provide a general survey, and for rapid interpolation, experimental results are presented also in the form of two diagrams, in which isobars and isotherms of the thermal conductivity are shown, using temperature and pressure, respectively, as the independent variables. Low pressure, gas phase data of previous observers and those of this research have been reduced to 1 atm with the aid of pressure coefficients derived from this study. Using the relation for the thermal conductivity of polar gases, proposed by Mason and Monchick, the results of all sources have been satisfactorily correlated between 300° and 500°K. The results of this work agree well with the few dense gas phase data reported by Keyes, and are in perfect agreement with tentative data along a short section of the saturation line given by Sellschopp in the only reference found on the thermal conductivity of liquid ammonia. Considering all known causes of error, the accuracy of this study is estimated to be within ±1.5 per cent for the liquid and dense gas phases, and within ±2 per cent for the low-pressure gas phase and the near-critical region.