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.

TIME-REVERSAL DUALITY AND PLANAR LATTICE DUALITY IN NON-EQUILIBRIUM LATTICE MODELS

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 285-292
Author(s):  
MAKOTO KATORI
Keyword(s):  
Phase Transitions ◽  
Time Reversal ◽  
Nearest Neighbor ◽  
Contact Process ◽  
Detailed Balance ◽  
Equilibrium Phase ◽  
Lattice Models ◽  
Dimensional System ◽  
Planar Lattice ◽  
Non Equilibrium

The contact process (CP) is a simple mathematical model for the spread of infection of a contagious disease. Though it has only nearest-neighbor interactions, phase transitions occur even in the one-dimensional system and non-equilibrium stationary states appear in supercritical phase. This implies violation of detailed balance. The appearance of such non-equilibrium states is related to directed percolation problems on the spatiotemporal plane. In the present paper, we study discretetime versions of the CP, the two-neighbor stochastic cellular automata (SCA), and clarify this viewpoint. We use two kinds of duality relations, the time-reversal duality and the planar lattice duality on the spatio-temporal plane, and give a good lower bound for the critical line of non-equilibrium phase transitions in the two-neighbor SCA.

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 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 An example of resonances, coherent structures and topological phase transitions - the origin of the low frequency broadband spectrum in the auroral zone

2001 ◽  
Vol 8 (3) ◽  
pp. 175-180 ◽  
Author(s):  
T. Chang
Keyword(s):  
Phase Transitions ◽  
Coherent Structures ◽  
Equilibrium Phase ◽  
Low Frequency ◽  
Auroral Zone ◽  
Point Of View ◽  
Topological Phase ◽  
Intermittent Turbulence ◽  
Self Organized Criticality ◽  
Topological Phase Transitions

Abstract. We consider the phenomena of intermittent turbulence in magnetized space plasmas from the point of view of topological phase transitions involving the merging and interactions of anisotropic coherent structures. The stochastic behaviour of these coherent plasma structures can undergo complex changes as the dynamic system evolves, similar to those commonly observed in (first and second order) equilibrium phase transitions. When conditions are favourable, such topological entities can evolve into a state of forced and/or self-organized criticality (FSOC). As an example, we apply these ideas to the understanding of the origin of the commonly observed broadband power-law low frequency electric field spectral densities and the characteristic filamentary current structures in the auroral zone. The broadband turbulence can provide efficient resonant energization of the ionospheric oxygen ions.

Equilibrium and non-equilibrium phase transitions in copolymer polyelectrolyte hydrogels

1997 ◽  
Vol 107 (5) ◽  
pp. 1645-1654 ◽  
Author(s):  
Anthony E. English ◽  
Toyoichi Tanaka ◽  
Elazer R. Edelman
Keyword(s):  
Phase Transitions ◽  
Equilibrium Phase ◽  
Non Equilibrium

Non-Equilibrium Phase Transitions and Living Organisms

2016 ◽  
Author(s):  
Maria Pilar Buera ◽  
Yrjö Roos ◽  
Harry Levine ◽  
Louise Slade ◽  
Horacio R. Corti ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Equilibrium Phase ◽  
Living Organisms ◽  
Non Equilibrium
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