Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks

TL;DR

This paper investigates phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models, revealing how directed percolation-like transitions influence critical exponents and the effects of external magnetic fields.

Contribution

It provides numerical analysis of critical exponents and explores the impact of external magnetic fields using generalized mean field approximation, highlighting differences from Glauber-Ising models.

Findings

Strong influence of PC transition on spin critical exponents

Drastic changes due to hyperscaling law from directed percolation

External magnetic field induces DP-type critical behaviour

Abstract

One-dimensional non-equilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest-neighbour spin exchanges exhibiting directed percolation-like parity conserving(PC) phase transition on the level of kinks are now further investigated, numerically, from the point of view of the underlying spin system. Critical exponents characterising its statics and dynamics are reported. It is found that the influence of the PC transition on the critical exponents of the spins is strong and the origin of drastic changes as compared to the Glauber-Ising case can be traced back to the hyperscaling law stemming from directed percolation(DP). Effect of an external magnetic field, leading to DP-type critical behaviour on the level of kinks, is also studied, mainly through the generalised mean field approximation.