Nonequilibrium Phase Transitions in Lattice Systems

Nonequilibrium phase transitions in lattice systems arise when a spatially extended, driven system undergoes a qualitative change between distinct steady states, often an active phase with sustained dynamics and an absorbing state from which no further evolution is possible. Unlike equilibrium transitions governed by free‐energy minimisation, these critical phenomena are controlled by dynamical rules, fluctuations and conservation laws. Lattice models such as reaction–diffusion processes, contact processes and epidemic spreading on regular or disordered grids serve as paradigms. Central concepts include universality classes—most prominently directed percolation—characterised by scaling exponents that depend only on general features like dimensionality and symmetries. Disorder and long‐range interactions can give rise to Griffiths phases, where rare regions dominate dynamics, or to hybrid transitions combining continuous and discontinuous behaviour. Strong‐disorder renormalisation group techniques, Monte Carlo simulations and field‐theoretic approaches have all advanced our understanding, with applications ranging from epidemic forecasting and neural activity to driven colloidal suspensions and catalytic reactions.

Research from Nature Portfolio

Recent studies of a one‐dimensional susceptible–infected–refractory–susceptible model on a regular lattice have revealed two separate nonequilibrium thresholds. At low infection probability the transition falls into the directed percolation class, whereas at high infection probability a discontinuous absorbing transition emerges, its sensitivity to initial conditions confirmed by finite‐size analysis and quasistationary distributions. In parallel, work on disordered contact processes has shown that at criticality the dominant active region can be a single, spatially disconnected cluster. By applying an asymptotically exact renormalisation group technique in one, two and three dimensions, researchers demonstrated that both classical and quantum disordered models exhibit magnetic or infection clusters that are highly correlated yet physically separated, challenging conventional notions of critical connectivity.

Nonequilibrium Phase Transitions in Lattice Systems publication trend

The graph below shows the total number of articles in nonequilibrium phase transitions in lattice systems across all publications each year (not limited to Nature Index journals).

Technical terms

Nonequilibrium phase transition: A transition between distinct steady states in a driven system, not described by equilibrium thermodynamics.

Absorbing state: A configuration with no escape under the system’s dynamics, often corresponding to zero activity.

Directed percolation: The paradigmatic universality class for transitions into absorbing states, featuring anisotropic spreading of activity.

Griffiths phase: An extended region near criticality in disordered systems where rare regions induce slow, power‐law dynamics.

Strong‐disorder renormalisation group (SDRG): An analytical scheme that systematically decimates the strongest local terms to reveal critical behaviour in disordered models.

References

1. Nonequilibrium phase transition of a one dimensional system reaches the absorbing state by two different ways. Scientific Reports (2023).
2. Renormalization theory of disordered contact processes with heavy-tailed dispersal. Physical Review Research (2023).
3. Subdiffusive Activity Spreading in the Diffusive Epidemic Process. Physical Review Letters (2022).
4. Emergence of disconnected clusters in heterogeneous complex systems. Scientific Reports (2020).
5. Flux-conserving directed percolation. Journal of Physics A: Mathematical and Theoretical (2024).