Equilibrium phase transitions in a porous medium

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.

Download Full-text

Crystallization of Binary Alloys and Non-Equilibrium Phase Transitions

Доклады Академии наук ◽

10.31857/s0869-56524896545-551 ◽

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.

Download Full-text

Mixed-order phase transition in a colloidal crystal

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1712584114 ◽

2017 ◽

Vol 114 (49) ◽

pp. 12906-12909 ◽

Cited By ~ 10

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.

Download Full-text