scholarly journals MEAN-FIELD CRITICAL BEHAVIOR AND ERGODICITY BREAK IN A NONEQUILIBRIUM ONE-DIMENSIONAL RSOS GROWTH MODEL

2012 ◽  
Vol 23 (03) ◽  
pp. 1250019 ◽  
Author(s):  
J. RICARDO G. MENDONÇA
Keyword(s):  
Phase Transition ◽  
Probability Density ◽  
Critical Behavior ◽  
Random Number Generator ◽  
Mean Field ◽  
System Size ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Roughening Transition ◽  
Pseudo Random Number Generator

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg–Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behavior. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behavior as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in the appendix a good and simple pseudo-random number generator used in our simulations.

Critical behavior of percolation and Markov fields on branching planes

1993 ◽  
Vol 30 (3) ◽  
pp. 538-547 ◽  
Author(s):  
C. Chris Wu
Keyword(s):  
Continuous Function ◽  
Critical Behavior ◽  
Mean Field ◽  
Percolation Model ◽  
Homogeneous Tree ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Percolation Probability ◽  
Triangle Condition ◽  
Markov Fields

For an independent percolation model on, whereis a homogeneous tree andis a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probabilityθ(p) is a continuous function ofpat the critical pointpc, and the critical exponents,γ,δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields onare also obtained.

scholarly journals Topological Frustration can modify the nature of a Quantum Phase Transition

2021 ◽  
Author(s):  
Vanja Marić ◽  
Gianpaolo Torre ◽  
Fabio Franchini ◽  
Salvatore Giampaolo
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Quantum Phase Transition ◽  
Landau Theory ◽  
Continuous Phase ◽  
Quantum Systems ◽  
Quantum Phase ◽  
Local Order ◽  
Ginzburg Landau ◽  
One Dimensional

Abstract Ginzburg-Landau theory of continuous phase transitions implicitly assumes that microscopic changes are negligible in determining the thermodynamic properties of the system. In this work we provide an example that clearly contrasts with this assumption. In particular, we consider the 2-cluster-Ising model, a one-dimensional spin-1/2 system that is known to exhibit a quantum phase transition between a magnetic and a nematic phase. By imposing boundary conditions that induce topological frustration we show that local order is completely destroyed on both sides of the transition and that the two thermodynamic phases can only be characterized by string order parameters. Having proved that topological frustration is capable of altering the nature of a system's phase transition, this result is a clear challenge to current theories of phase transitions in complex quantum systems.

Stochastic Properties of a One-Dimensional Discrete Ginzburg-Landau Field

1981 ◽  
Vol 36 (1) ◽  
pp. 1-9
Author(s):  
M. Jaspers ◽  
W. Schattke
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ginzburg Landau ◽  
Mean Values ◽  
One Dimensional ◽  
Slowing Down ◽  
Set Up ◽  
Stochastic Properties

Starting from a master equation for a discrete order parameter a dynamical model is set up via mean-field approximation in the Fokker-Planck equation. The time evolution of some mean values is calculated numerically, showing two transitions with characteristic slowing down of the relaxation time

FIELD-THEORETICAL CALCULATIONS ON THE HALDANE GAP OF QUASI-ONE-DIMENSIONAL HEISENBERG ANTIFERROMAGNETS

2009 ◽  
Vol 23 (31) ◽  
pp. 5789-5800
Author(s):  
HAI HUANG
Keyword(s):  
Finite Temperature ◽  
Theoretical Calculations ◽  
Mean Field ◽  
Zero Temperature ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Field Approach ◽  
Haldane Gap ◽  
Chain Theory ◽  
Heisenberg Antiferromagnets

One-dimensional Heisenberg antiferromagnets can be described by the O (3) nonlinear σ-model (NLσM). We give a review on zero temperature and finite temperature Haldane gaps obtained from this model. Based on the coupled-chain theory, we derive the finite temperature Haldane gap for triangular antiferromagnet RbNiCl 3. The Néel temperature is obtained as 11 K. In order to treat the anisotropy in crystal Ni ( C 2 H 8 N 2)2 NO 2( ClO 4), we relax the constraint of the NLσM and compute the finite temperature Haldane gap using a Ginzburg–Landau mean field approach. The comparison with the experimental data is discussed.

Critical Behavior of Gd5Si2Ge1.9Ga0.1 near the Ferromagnetic-Paramagnetic Phase Transition

2013 ◽  
Vol 873 ◽  
pp. 855-860 ◽  
Author(s):  
Zeng Ru Zhao ◽  
Gao Feng Wang ◽  
Xue Feng Zhang
Keyword(s):  
Phase Transition ◽  
Critical Behavior ◽  
Scaling Law ◽  
Mean Field Theory ◽  
Mean Field ◽  
Entropy Change ◽  
Paramagnetic Phase ◽  
Range Type ◽  
Fisher Model ◽  
The Mean

The critical behavior near the ferromagnetic-paramagnetic phase transition in Gd5Si2Ge1.9Ga0.1 has been investigated using a method based on the field dependence of isothermal entropy change. The reliability of the critical exponents determined in such a way has been examined through various techniques, like constructing the modified Arrott plot, applying the scaling law on the isothermal magnetization curves, and comparing the values with those obtained from the Kouvel-Fisher model. The resulting values of the exponents were estimated to be = 0.45(2), = 1.31(5), = 3.9(2) and = 0.69(1), close to the values predicted by the mean field theory. Hence, we concluded that the exchange interaction is of long-range type.

scholarly journals The inactive–active phase transition in the noisy additive (exclusive-or) probabilistic cellular automaton

2015 ◽  
Vol 27 (02) ◽  
pp. 1650016 ◽  
Author(s):  
J. Ricardo G. Mendonça
Keyword(s):  
Phase Transition ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Transition Probabilities ◽  
Mean Field ◽  
Active Phase ◽  
Mean Field Equations ◽  
Probabilistic Cellular Automaton ◽  
The Mean ◽  
Exclusive Or

We investigate the inactive–active phase transition in an array of additive (exclusive-or) cellular automata (CA) under noise. The model is closely related with the Domany-Kinzel (DK) probabilistic cellular automaton (PCA), for which there are rigorous as well as numerical estimates on the transition probabilities. Here, we characterize the critical behavior of the noisy additive cellular automaton by mean field analysis and finite-size scaling and show that its phase transition belongs to the directed percolation universality class of critical behavior. As a by-product of our analysis, we argue that the critical behavior of the noisy elementary CA 90 and 102 (in Wolfram’s enumeration scheme) must be the same. We also perform an empirical investigation of the mean field equations to assess their quality and find that away from the critical point (but not necessarily very far away) the mean field approximations provide a reasonably good description of the dynamics of the PCA.

Critical behavior of percolation and Markov fields on branching planes

1993 ◽  
Vol 30 (03) ◽  
pp. 538-547 ◽  
Author(s):  
C. Chris Wu
Keyword(s):  
Continuous Function ◽  
Critical Behavior ◽  
Mean Field ◽  
Percolation Model ◽  
Homogeneous Tree ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Percolation Probability ◽  
Triangle Condition ◽  
Markov Fields

For an independent percolation model on , where is a homogeneous tree and is a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probability θ (p) is a continuous function of p at the critical point p c, and the critical exponents , γ, δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields on are also obtained.

THEORY OF PHOTOINDUCED PHASE TRANSITION IN THE QUASI-ONE-DIMENSIONAL CHARGE TRANSFER COMPOUND TTF-CA

2001 ◽  
Vol 15 (28n30) ◽  
pp. 3714-3717 ◽  
Author(s):  
P. HUAI ◽  
K. NASU
Keyword(s):  
Phase Transition ◽  
Charge Transfer ◽  
Mean Field ◽  
Lattice Relaxation ◽  
Coulomb Interactions ◽  
Single Charge ◽  
One Dimensional ◽  
The Mean ◽  
A Charge ◽  
Franck Condon

We theoretically study the photoinduced ionic→neutral phase transition in the quasi-one-dimensional molecular crystal TTF-CA. Our theoretical model includes strong intra-chain Coulomb interactions as well as very weak inter-chain interactions. Within the mean-field picture, we investigate the nonlinear lattice relaxation of a charge transfer exciton, and clarify the adiabatic path from its Franck-Condon state to a macroscopic neutral domain. It is found that the lowest state of such a single charge transfer exciton can not relax down to the neutral domain straightly, but a large excess energy is necessary so that it can overcome a high barrier. The aggregation of two identically shaped neutral domains is also discussed.

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