Multiscaling and the classification of continuous phase transitions

1992 ◽  
Vol 68 (2) ◽  
pp. 190-192 ◽  
Author(s):  
R. Hilfer
Keyword(s):  
Phase Transitions ◽  
Continuous Phase

scholarly journals Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5

2015 ◽  
Vol 112 (3) ◽  
pp. 673-678 ◽  
Author(s):  
Lin Jiao ◽  
Ye Chen ◽  
Yoshimitsu Kohama ◽  
David Graf ◽  
E. D. Bauer ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Fermi Surface ◽  
Quantum Phase Transitions ◽  
Continuous Phase ◽  
Multiple Quantum ◽  
Quantum Critical Points ◽  
Thermally Driven ◽  
Significant Step ◽  
Open Issues

Conventional, thermally driven continuous phase transitions are described by universal critical behavior that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behavior remain open issues. Here we report measurements of heat capacity and de Haas–van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B0* ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn5 suggest that the Fermi-surface change at B0* is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn5, a significant step toward the derivation of a universal phase diagram for QCPs.

Classification of continuous phase transitions and stable phases. I. Six-dimensional order parameters

1986 ◽  
Vol 33 (3) ◽  
pp. 1774-1788 ◽  
Author(s):  
Jai Sam Kim ◽  
Dorian M. Hatch ◽  
Harold T. Stokes
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Order Parameters

Classification of continuous phase transitions and stable phases. II. Four-dimensional order parameters

1986 ◽  
Vol 33 (9) ◽  
pp. 6210-6230 ◽  
Author(s):  
Jai Sam Kim ◽  
Harold T. Stokes ◽  
Dorian M. Hatch
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Order Parameters

scholarly journals Empirical evidence reveals the phase diagram of patch patterns in Mediterranean drylands

2017 ◽  
Author(s):  
Fernando Meloni ◽  
Cristiano R. F. Granzotti ◽  
Alexandre S. Martinez
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Satellite Images ◽  
A Priori ◽  
Continuous Phase ◽  
Adequate Description ◽  
Scaling Exponents ◽  
Open Issue ◽  
The Subject ◽  
Ecological Functioning

AbstractDrylands are ecosystems with limited water resources, often subjected to desertification. Conservation and restoration efforts towards these ecosystems depend on the interplay between ecological functioning and spatial patterns formed by local vegetation. Despite recent advances on the subject, an adequate description of phase transitions between the various vegetated phases remains an open issue. Here, we gather vegetation data of drylands from Southern Spain using satellite images. Our findings support three vegetated phases, separated by two distinct phase transitions, including a continuous phase transition, with new relations between scaling exponents of ecological variables. The phase diagram is obtained without a priori assumption about underlying ecological dynamics. We apply our analysis to a different dryland system in the Western United States and verify a compatible critical behavior, in agreement with the universality hypothesis.

SCALING THEORY AND THE CLASSIFICATION OF PHASE TRANSITIONS

1992 ◽  
Vol 06 (13) ◽  
pp. 773-784 ◽  
Author(s):  
R. HILFER
Keyword(s):  
Phase Transitions ◽  
Statistical Physics ◽  
Thermodynamic Description ◽  
Classification Theory ◽  
Nonequilibrium Phase Transitions ◽  
Critical Limit ◽  
Scaling Hypothesis ◽  
Recent Classification ◽  
Thermodynamics And Statistical Mechanics

The recent classification theory for phase transitions (R. Hilfer, Physica Scripta 44, 321 (1991)) and its relation with the foundations of statistical physics is reviewed. First it is outlined how Ehrenfests classification scheme can be generalized into a general thermodynamic classification theory for phase transitions. The classification theory implies scaling and multiscaling thereby eliminating the need to postulate the scaling hypothesis as a fourth law of thermodynamics. The new classification has also led to the discovery and distinction of nonequilibrium transitions within equilibrium statistical physics. Nonequilibrium phase transitions are distinguished from equilibrium transitions by orders less than unity and by the fact that equilibrium thermodynamics and statistical mechanics become inapplicable at the critical point. The latter fact requires a change in the Gibbs assumption underlying the canonical and grandcanonical ensembles in order to recover the thermodynamic description in the critical limit.

Continuous phase transitions in molecules: BeF2

1981 ◽  
Vol 85 (5) ◽  
pp. 271-272 ◽  
Author(s):  
M.A.F. Gomes
Keyword(s):  
Phase Transitions ◽  
Continuous Phase

Green Function Calculations of Properties for the Magnetocaloric Layered Structures Based Upon FeMnAsP

SPIN ◽  
2016 ◽  
Vol 06 (03) ◽  
pp. 1650010
Author(s):  
Osvaldo F. Schilling
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Green Function ◽  
Landau Theory ◽  
Random Phase ◽  
Layered Structures ◽  
Continuous Phase ◽  
Theoretical Treatment ◽  
Entropy Variation ◽  
Commercial Applications

The alternating Fe–Mn layered structures of the compounds FeMnAsxP[Formula: see text] display properties which have been demonstrated experimentally as very promising as far as commercial applications of the magnetocaloric effect are concerned. However, the theoretical literature on this and other families of magnetocaloric compounds still adopts simple molecular-field models in the description of important statistical mechanical properties like the entropy variation that accompanies applied isothermal magnetic field cycling, as well as the temperature variation following adiabatic magnetic field cycles. In the present paper, a random phase approximation Green function theoretical treatment is applied to such structures. The advantages of such approach are well known since the details of the crystal structure are easily incorporated in the model, as well as a precise description of correlations between neighbor spins can be obtained. We focus on a simple one-exchange parameter Heisenberg model, and the observed first-order phase transitions are reproduced by the introduction of a biquadratic term in the Hamiltonian whose origin is related both to the magnetoelastic coupling with the phonon spectrum in these compounds as well as with the values of spins in the Fe and Mn ions. The calculations are compared with experimental magnetocaloric data for the FeMnAsxP[Formula: see text] compounds. In particular, the magnetic field dependence for the entropy variation at the transition temperature predicted from the Landau theory of continuous phase transitions is reproduced even in the case of discontinuous transitions.

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