Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics

Abstract

When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. We present a brief review of some of the new insights garnered and some of the outstanding puzzles, as well as speculate on the model's role in the future of non-equilibrium statistical physics.

3 figures. Proceedings of 100th Statistical Mechanics Meeting, Rutgers, NJ (December, 2008)

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Cited by in corpus (23)

• Non-equilibrium quasi-condensates in reduced dimensions
• Phase separation and large deviations of lattice active matter
• Non-equilibrium fixed points of coupled Ising models
• On the microscopic origin and macroscopic implications of lane formation in mixtures of oppositely-driven particles
• Approximate thermodynamic structure for driven lattice gases in contact
• Activity-induced phase transition in a quantum many-body system
• Nonequilibrium steady states in contact: Approximate thermodynamic structure and zero-th law for driven lattice gases
• Dynamics of the directed Ising chain
• Dynamics of Repulsion Processes
• Strongly anisotropic non-equilibrium phase transition in Ising models with friction
• Flux and storage of energy in non-equilibrium, stationary states
• Driving Driven Lattice Gases to Identify Their Universality Classes
• Collective transport of weakly interacting molecular motors with Langmuir kinetics
• Phase Diagram for a 2-D Two-Temperature Diffusive XY Model
• Sheared Ising models in three dimensions
• Short-time Behaviour and Criticality of Driven Lattice Gases
• Thermodynamic Theory of Phase Transitions in Driven Lattice Gases
• Nonequilibrium chemical potentials of steady-state lattice gas models in contact: A large-deviations approach
• Product blocking measures and a particle system proof of the Jacobi triple product
• Simulations of driven and reconstituting lattice gases
• Damage Spreading in a Driven Lattice Gas Model
• Non-additive large deviations function for the particle densities of driven systems in contact
• "Cracking-the-whip" effect stretches driven polymers