Tendency toward crossover of the effective susceptibility exponent from its doubled Ising value to its doubled mean-field value near a double critical point

2008 ◽  
Vol 129 (13) ◽  
pp. 134506 ◽  
Author(s):  
U. K. Pradeep
Keyword(s):  
Critical Point ◽  
Mean Field ◽  
Double Critical Point

New results on the dynamics of Rochelle salt crystals (a system with a "double" critical point)

1986 ◽  
Vol 149 (6) ◽  
pp. 331 ◽  
Author(s):  
A.A. Volkov ◽  
Georgii V. Kozlov ◽  
E.B. Kryukova ◽  
A.A. Sobyanin
Keyword(s):  
Critical Point ◽  
Rochelle Salt ◽  
Salt Crystals ◽  
Double Critical Point

Structure of Cd-Ga Melts Part 2: X-Ray Small-Angle Scattering

1980 ◽  
Vol 35 (9) ◽  
pp. 938-945 ◽  
Author(s):  
Gerhard Hermann ◽  
Georg Rainer-Harbach ◽  
Siegfried Steeb
Keyword(s):  
Critical Point ◽  
Small Angle ◽  
Lattice Gas ◽  
Critical Concentration ◽  
Mean Field Theory ◽  
Mean Field ◽  
Small Angle Scattering ◽  
Correlation Lengths ◽  
X Ray ◽  
Angle Scattering

Abstract X-ray small-angle scattering experiments were performed on nine melts of the Cd-Ga system at different temperatures up to 440°C. Evaluation of the data follows the Ornstein-Zernike theory of critical scattering, thus yielding correlation lengths ξ of concentration fluctuations and the long-wavelength limit Sec (0) of the Bhatia-Thornton structure factor. Studies of the concentration and temperature dependence of ξ and SCC (0) indicate that the critical point occurs at cc = 50.0 ± 1-0 at % Ga and Tc - 295.2 ± 0-1° C. For a melt with the critical concentration, SCC (0) increases up to 3500 times the ideal S1dCC (0)=CACB-This indicates a strong segregation tendency. In the vicinity of the critical point of the Cd-Ga system, experimental correlation lengths ξ > 100 A were obtained. The critical-point exponents ν and γ were determined. It follows that the behaviour of a critical Cd-Ga melt satisfies the prediction of the classical mean-field theory for higher temperatures, whereas, within experimental accuracy, the lattice-gas predictions are satisfied upon approaching the critical temperature.

Behaviour of the curve of critical exponents near and away from a double critical point

1993 ◽  
Vol 181 (6) ◽  
pp. 471-475 ◽  
Author(s):  
B.V. Prafulla ◽  
A. Kumar ◽  
E.S.R. Gopal
Keyword(s):  
Critical Point ◽  
Critical Exponents ◽  
Double Critical Point

GROSS–WITTEN POINT AND DECONFINEMENT

2005 ◽  
Vol 20 (19) ◽  
pp. 4469-4474 ◽  
Author(s):  
ROBERT D. PISARSKI
Keyword(s):  
Phase Transition ◽  
Gauge Theory ◽  
Critical Point ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
First Order

Following Aharony et al., we analyze the deconfining phase transition in a SU(∞) gauge theory in mean field approximation. The Gross–Witten model emerges as an "ultra"-critical point for deconfinement: while thermodynamically of first order, masses vanish, asymmetrically, at the transition. Potentials for N = 3 are also shown.

Truncation theorems for spinodals and critical points of mean-field models for polydisperse polymer solutions

1981 ◽  
Vol 375 (1762) ◽  
pp. 397-408 ◽  
Keyword(s):  
Molecular Weight ◽  
Critical Point ◽  
Molecular Weight Distribution ◽  
Weight Distribution ◽  
Polymer Solutions ◽  
Mathematical Proof ◽  
Mean Field ◽  
Combinatorial Theory ◽  
Mean Field Models ◽  
Polydisperse Polymer

An exact truncation theorem is proved for the expansion, in terms of moments of the molecular weight distribution, of the Gibbs spinodal determinants of a wide class of generalized mean-field Flory-Huggins models for polydisperse polymer solutions. A similar truncation theorem for the critical-point determinants is derived on the assumption that an expansion in a finite number of moments exists. These truncations have been exploited elsewhere through the relative economy they confer on computations involved in the testing and refinement of such theoretical models by fitting them to experimental data. A much simplified general and explicit expression is found for the relevant spinodal determinants of the mean-field models. If the relevant free energy of mixing is assumed to depend on the moments M 0 , M 1 , . . . , M n of the molecular weight distribution, this expression shows the spinodal to be a function of M 0 , M 1 , . . , M 2 n +1 . The critical point is a function of M 0 , M 1 , . . . , M 3 n +2 . The truncations at M 2 n +1 and M 3 n +2 betoken a collapse to a small subspace of the formal Hilbert-space representation of the composition space of the solution. The mathematical proof follows the pathway of the classical routes to the rigorous theory of function spaces opened up by von Koch and Fredholm, and the spinodal expression bears the imprint of a classical solution of Stieltje’s moment problem. In addition, modern operational methods of combinatorial theory are relevant to future extensions of the present work. Theoreticians may, therefore, be interested to come to the aid of experimentalists struggling with the analysis of data of much practical import.

Light scattering near a double critical point: Evidence for crossover behavior

1992 ◽  
Vol 45 (2) ◽  
pp. 1266-1269 ◽  
Author(s):  
B. V. Prafulla ◽  
T. Narayanan ◽  
A. Kumar
Keyword(s):  
Light Scattering ◽  
Critical Point ◽  
Crossover Behavior ◽  
Double Critical Point

scholarly journals Perturbation about the mean field critical point

1982 ◽  
Vol 86 (3) ◽  
pp. 337-362 ◽  
Author(s):  
Jean Bricmont ◽  
Jean-Raymond Fontaine ◽  
Eugene Speer
Keyword(s):  
Critical Point ◽  
Mean Field ◽  
The Mean

scholarly journals Emergent $${{{{{{{\mathcal{PT}}}}}}}}$$-symmetry breaking of collective modes with topological critical phenomena

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Jian-Song Pan ◽  
Wei Yi ◽  
Jiangbin Gong
Keyword(s):  
Symmetry Breaking ◽  
Critical Point ◽  
Critical Phenomenon ◽  
Mean Field ◽  
Low Frequency ◽  
Spontaneous Breaking ◽  
Collective Modes ◽  
Spin Orbit Coupling ◽  
External Perturbations ◽  
Spectral Topology

AbstractThe spontaneous breaking of parity-time ($${{{{{{{\mathcal{PT}}}}}}}}$$ PT ) symmetry yields rich critical behavior in non-Hermitian systems, and has stimulated much interest, albeit most previous studies were performed within the single-particle or mean-field framework. Here, by studying the collective excitations of a Fermi superfluid with $${{{{{{{\mathcal{PT}}}}}}}}$$ PT -symmetric spin-orbit coupling, we uncover an emergent $${{{{{{{\mathcal{PT}}}}}}}}$$ PT -symmetry breaking in the Anderson-Bogoliubov (AB) collective modes, even as the superfluid ground state retains an unbroken $${{{{{{{\mathcal{PT}}}}}}}}$$ PT symmetry. The critical point of the transition is marked by a non-analytic kink in the speed of sound, which derives from the coalescence and annihilation of the AB mode and its hole partner, reminiscent of the particle-antiparticle annihilation. The system consequently becomes immune to low-frequency external perturbations at the critical point, a phenomenon associated with the spectral topology of the complex quasiparticle dispersion. This critical phenomenon offers a fascinating route toward perturbation-free quantum states.

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