Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/9706114 · Journal of Statistical Physics

First-Order Phase Transitions in One-Dimensional Steady States

Peter F. Arndt, Thomas Heinzel, Vladimir Rittenberg

Published Feb 1, 1998• 60 citations
arXivHTMLPDF
DOI
10.1023/a:1023229004414

Related papers

First-order phase transition in an approximately one-dimensional system

V. N. Bogomolov, E.V. Kolla, Yu. A. Kumzerov

ZhETF Pisma Redaktsiiu•Jan 1, 1985•3 citations

First order phase transition in coupled one dimensional systems

Janine Lajzerowicz, Jean–Pierre Françoise

Annals of the Israel Physical Society•Jan 1, 1978•0 citations

First-order phase transitions in one-dimensional steady states

Peter F. Arndt, Thomas Heinzel, V. Rittenberg

The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godrèche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function but looks like a standard Ginzburg-Landau picture. If a symmetry breaking term is introduced in the boundaries the Ginzburg-Landau picture remains and one obtains spinodal points. The spectrum of the hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the firstorder phase transition line with a dynamical critical exponent z = 2 as expected from the existence of shocks and at the spinodal points where we find z = 1. It is for the first time that this value which characterizes conformal invariant equilibrium problems appears in stochastic processes. cond-mat/9706114

•Jan 1, 1997•57 citations

Finite-size scaling and universality for the totally asymmetric simple-exclusion process

J.G. Brankov, Nadezhda Bunzarova

The applicability of the concepts of finite-size scaling and universality to nonequilibrium phase transitions is considered in the framework of the one-dimensional totally asymmetric simple-exclusion process with open boundaries. In the thermodynamic limit there are boundary-induced transitions both of the first and second order between steady-state phases of the model. We derive finite-size scaling expressions for the current near the continuous phase transition and for the local density near the first-order transition under different stochastic dynamics and compare them to establish the existence of universal functions. Next we study numerically the finite-size behavior of the Lee-Yang zeros of the normalization factor for the different steady-state probabilities.

Physical Review E•Mar 22, 2005•12 citations

First-Order Phase Transitions

Wolfhard Janke E

Springer eBooks•Jan 1, 2003•33 citations

Phase transitions in one dimension and less

Paul Fendley, Oleg Tchernyshyov

arXiv:cond-mat/0202129•Nuclear Physics B•Sep 1, 2002•3 citations
The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godrèche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function but looks like a standard Ginzburg-Landau picture. If a symmetry breaking term is introduced in the boundaries the Ginzburg-Landau picture remains and one obtains spinodal points. The spectrum of the hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the firstorder phase transition line with a dynamical critical exponent z = 2 as expected from the existence of shocks and at the spinodal points where we find z = 1. It is for the first time that this value which characterizes conformal invariant equilibrium problems appears in stochastic processes. cond-mat/9706114
The applicability of the concepts of finite-size scaling and universality to nonequilibrium phase transitions is considered in the framework of the one-dimensional totally asymmetric simple-exclusion process with open boundaries. In the thermodynamic limit there are boundary-induced transitions both of the first and second order between steady-state phases of the model. We derive finite-size scaling expressions for the current near the continuous phase transition and for the local density near the first-order transition under different stochastic dynamics and compare them to establish the existence of universal functions. Next we study numerically the finite-size behavior of the Lee-Yang zeros of the normalization factor for the different steady-state probabilities.