Shock probes in a one-dimensional Katz-Lebowitz-Spohn model

TL;DR

This study investigates shock probes in a one-dimensional driven diffusive system with Ising interactions, finding that the decay exponents of correlation functions are largely unaffected by the interaction strength, contrary to previous approximate predictions.

Contribution

The paper provides numerical evidence that static and dynamical correlation exponents remain constant across a range of Ising interaction strengths, challenging earlier approximate mappings.

Findings

Exponents remain constant over a range of interaction strengths

Correlation functions decay similarly to the non-interacting case

Large-scale properties are unaffected by short-range Ising interactions

Abstract

We consider shock probes in a one-dimensional driven diffusive medium with nearest neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterising the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.