scholarly journals Mixed-order phase transition in a colloidal crystal

2017 ◽  
Vol 114 (49) ◽  
pp. 12906-12909 ◽  
Author(s):  
Ricard Alert ◽  
Pietro Tierno ◽  
Jaume Casademunt
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Colloidal Particles ◽  
Colloidal Crystal ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Dimension ◽  
Colloidal System ◽  
Test Bed ◽  
Mixed Order

Mixed-order phase transitions display a discontinuity in the order parameter like first-order transitions yet feature critical behavior like second-order transitions. Such transitions have been predicted for a broad range of equilibrium and nonequilibrium systems, but their experimental observation has remained elusive. Here, we analytically predict and experimentally realize a mixed-order equilibrium phase transition. Specifically, a discontinuous solid–solid transition in a 2D crystal of paramagnetic colloidal particles is induced by a magnetic field H. At the transition field Hs, the energy landscape of the system becomes completely flat, which causes diverging fluctuations and correlation length ξ∝|H2−Hs2|−1/2. Mean-field critical exponents are predicted, since the upper critical dimension of the transition is du=2. Our colloidal system provides an experimental test bed to probe the unconventional properties of mixed-order phase transitions.

scholarly journals Response theory and phase transitions for the thermodynamic limit of interacting identical systems

2020 ◽  
Vol 476 (2244) ◽  
pp. 20200688
Author(s):  
Valerio Lucarini ◽  
Grigorios A. Pavliotis ◽  
Niccolò Zagli
Keyword(s):  
Phase Transitions ◽  
Thermodynamic Limit ◽  
Linear Response ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Critical Transitions ◽  
Autocorrelation Time ◽  
The Common ◽  
Fokker Planck Equations ◽  
Non Equilibrium

We study the response to perturbations in the thermodynamic limit of a network of coupled identical agents undergoing a stochastic evolution which, in general, describes non-equilibrium conditions. All systems are nudged towards the common centre of mass. We derive Kramers–Kronig relations and sum rules for the linear susceptibilities obtained through mean field Fokker–Planck equations and then propose corrections relevant for the macroscopic case, which incorporates in a self-consistent way the effect of the mutual interaction between the systems. Such an interaction creates a memory effect. We are able to derive conditions determining the occurrence of phase transitions specifically due to system-to-system interactions. Such phase transitions exist in the thermodynamic limit and are associated with the divergence of the linear response but are not accompanied by the divergence in the integrated autocorrelation time for a suitably defined observable. We clarify that such endogenous phase transitions are fundamentally different from other pathologies in the linear response that can be framed in the context of critical transitions. Finally, we show how our results can elucidate the properties of the Desai–Zwanzig model and of the Bonilla–Casado–Morillo model, which feature paradigmatic equilibrium and non-equilibrium phase transitions, respectively.

scholarly journals Crystallization of Binary Alloys and Non-Equilibrium Phase Transitions

2019 ◽  
Vol 489 (6) ◽  
pp. 545-551
Author(s):  
E. V. Radkevich ◽  
O. A. Vasil’eva ◽  
M. I. Sidorov
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Numerical Experiments ◽  
Binary Alloys ◽  
Equilibrium Phase ◽  
Homogeneous State ◽  
Nonequilibrium Phase Transition ◽  
Nonequilibrium Phase ◽  
Initial Stage ◽  
Melt Cooling

A model was constructed for the reconstruction of the initial stage of crystallization of binary alloys as a nonequilibrium phase transition, the mechanism of which is diffusion stratification. Numerical experiments were performed. Self-excitation of a homogeneous state by the edge control melt cooling condition.

FLUCTUATION EFFECTS IN A CLASS OF SYSTEMS WITH TWO ORDER PARAMETERS

1993 ◽  
Vol 07 (27) ◽  
pp. 1725-1731 ◽  
Author(s):  
L. DE CESARE ◽  
I. RABUFFO ◽  
D.I. UZUNOV
Keyword(s):  
Phase Transition ◽  
Renormalization Group ◽  
Phase Transitions ◽  
Order Phase Transition ◽  
Mean Field ◽  
Ising Models ◽  
Order Parameters ◽  
The Mean ◽  
Fluctuation Effects ◽  
Second Order Phase Transition

The phase transitions described by coupled spin -1/2 Ising models are investigated with the help of the mean field and the renormalization group theories. Results for the type of possible phase transitions and their fluctuation properties are presented. A fluctuation-induced second-order phase transition is predicted.

scholarly journals Non-Equilibrium Phase Transitions Induced by Social Temperature In Kinetic Exchange Opinion Models on Regular Lattices

2017 ◽  
Vol 01 (01) ◽  
pp. 1740001 ◽  
Author(s):  
Nuno Crokidakis
Keyword(s):  
Phase Transitions ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Equilibrium Phase ◽  
Critical Dimension ◽  
Point Of View ◽  
Majority Opinion ◽  
Regular Lattices ◽  
Independent Behavior ◽  
Non Equilibrium

In this work, we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular [Formula: see text]-dimensional lattice has a probability [Formula: see text] to act as independent, i.e., he can choose his opinion independent of the opinions of his neighbors. Furthermore, with the complementary probability [Formula: see text], the agent interacts with a randomly chosen nearest neighbor through a kinetic exchange. Our numerical results suggest that the model undergoes non-equilibrium phase transitions at critical points [Formula: see text] that depend on the lattice dimension. These transitions are of order–disorder type, presenting the same critical exponents of the Ising model. The results also suggest that the upper critical dimension of the model is [Formula: see text], as for the Ising model. From the social point of view, with increasing number of social connections, it is easier to observe a majority opinion in the population.

Phase transitions and their devices

2017 ◽  
Author(s):  
Sandip Tiwari
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Mean Field ◽  
Electric Polarization ◽  
Disk Drives ◽  
Spin Correlations ◽  
Electron Phonon Coupling ◽  
Electron Correlation Effects ◽  
Property Changes ◽  
Ferroelectric Memories

Phase transitions as a collective response of an ensemble, with appearance of unique stable properties spontaneously, is critical to a variety of devices: electronic, magnetic, optical, and their coupled forms. This chapter starts with a discussion of broken symmetry and its manifestation in the property changes in thermodynamic phase transition and the Landau mean-field articulation. It then follows it with an exploration of different phenomena and their use in devices. The first is ferroelectricity—spontaneous electric polarization—and its use in ferroelectric memories. Electron correlation effects are explored, and then conductivity transition from electron-electron and electron-phonon coupling and its use in novel memory and device forms. This is followed by development of an understanding of spin correlations and interactions and magnetism—spontaneous magnetic polarization. The use and manipulation of the magnetic phase transition in disk drives, magnetic and spin-torque memory as well as their stability is explored. Finally, as a fourth example, amorphous-crystalline structural transition in optical, electronic, and optoelectronic form are analyzed. This latter’s application include disk drives and resistive memories in the form of phase-change as well as those with electochemical transport.

Physical Kinetics of Loop Quantum Gravity and Blackhole Dynamics: Kinetic Theory of Quantum Spacetime, Blackhole Phase Transition Theory and Blackhole Fission.

2015 ◽  
Vol 9 (1) ◽  
pp. 2322-2329
Author(s):  
Koustubh Kabe
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Kinetic Theory ◽  
Liquid Droplet ◽  
Equilibrium Phase ◽  
Top Physics ◽  
Experimental Tests ◽  
Spacetime Geometry ◽  
Kinetics Of ◽  
Quantum Spacetime

In the following chapter, a sincere endeavor is made to build  a physically as well as in most later aspects a mathematically simple but rigorous physical kinetics of spacetime and of blackholes. Starting with a 3-volume quantization result of the now standard Ashtekar-Lewandowski Quantum Riemannian Geometry, and based on the work of the author on time as a vortex, a 4-volume spacetime quantum, a rapidly fluctuating one is developed and the foundations seem to look shaky in the very beginning, but start to get stronger and stronger as one starts to enter the end of the section on the physical kinetics of blackholes. Thus, experimental tests and observational predictions have been made whenever seem required or appropriate for justification, examples from laboratory table-top physics provided. Once the framework of kinetic theory has been developed, the author has entered into the realm of blackhole phase transitions nucleating from backgroung spacetime as well as other blackhole phase transitions. The equations of phase transitions have been rigorously analyzed and physical interpretations and physical predictions provided. Also certain the Bardeen-Carter-Hawking standard zeroeth law of blackhole dynamics been deduced in the context of equilibrium phase transitions in blackholes. The possibility of splitting of the Kerr-Newman blackhole akin to nuclear fission is obtained. An interesting work is the conception and extensin of the stretched horizon which was constructed by Ashoke Sen in the context of unphysical extremal blackholes in string theory -to that of isolated horizons in the context of arbitrary blackholes as proposed by Rovelli . Quantum gravitational dispersion as well as diffraction of light and gravitational waves by discrete nature of quantum spacetime geometry has been predicted in phenomenology. The paper predicts the gravi-electric Meissner effect in the wake of the Galilean superconductivity in the form of locally Lorentzian spacetimes as a critical behavior in the context of a second order phase transition. The property of the blackholes to undergo fission is demonstrated in the equations of phase transitions. This is used to explain the astrophysical phenomenon of Quasars. An iso-Higgs multiplet is qualitatively predicted as basic constituents of the blackhole. A liquid droplet model is suggested to explain the newly predicted phenomenon of blackhole fission in this paper.The chapter as a whole builds the foundations of the subject of the title of the paper.

Formal conditions for non-equilibrium phase transitions in semiconductors

1979 ◽  
Vol 365 (1723) ◽  
pp. 511-521 ◽  
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Kinetic Models ◽  
Reaction Kinetic ◽  
Equilibrium Phase ◽  
Second Order ◽  
Systematic Search ◽  
Generation Mechanisms ◽  
Non Equilibrium

A systematic search is made for semiconductor models displaying non-equilibrium phase transitions induced by recombination and generation processes. Formal conditions are elaborated for some typical classes of reaction kinetic models with a phase transition. Under this aspect various recombination and generation mechanisms involving electrons, holes and traps are surveyed systematically, and subsequently two new classes of band–trap models exhibiting first and second order phase transitions, respectively, are constructed.

scholarly journals Nuclear Shell Model And Quantum Phase Transitions

2019 ◽  
Vol 26 ◽  
pp. 88
Author(s):  
S. Karampagia ◽  
V. Zelevinsky
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Shell Model ◽  
Quantum Phase Transitions ◽  
Mean Field ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Orbital Space ◽  
Nuclear Shell

The usual nuclear shell model defines nuclear properties through an effective mean-field plus a two-body interaction Hamiltonian in a finite orbital space. In this study we try to understand the correlation between the various parts of the shell model Hamiltonian and the nuclear observables and collectivity in nuclei. By varying specific groups of matrix elements we find signs of a phase transition in nuclei between a non-collective and a collective phase. In all cases studied the collective phase is attained when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, giving collective characteristics to nuclei.

scholarly journals TELESCOPIC LINKAGES AND A TOPOLOGICAL APPROACH TO PHASE TRANSITIONS

2011 ◽  
Vol 90 (2) ◽  
pp. 183-195 ◽  
Author(s):  
MICHAEL FARBER ◽  
VIKTOR FROMM
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Configuration Space ◽  
Betti Number ◽  
Statistical Physics ◽  
Betti Numbers ◽  
Equilibrium Phase ◽  
Mean Field ◽  
Exponential Growth Rate ◽  
Topological Approach

AbstractA topological approach to the theory of equilibrium phase transitions in statistical physics is based on the topological hypothesis, which claims that phase transitions are due to changes of the topology of suitable submanifolds in the configuration space. In this paper we examine in detail the antiferromagnetic mean-field XY model and study the topology of the subenergy manifolds. The latter can be interpreted mechanically as the configuration space of a linkage with one telescopic leg. We use methods of Morse theory to describe explicitly the Betti numbers of this configuration space. We apply these results to the antiferromagnetic mean-field XY model and compute the exponential growth rate of the total Betti number. Previous authors studied the Euler characteristic rather than the total Betti number. We show that in the presence of an external magnetic field the model undergoes a single ‘total Betti number phase transition’.

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