An alternative order-parameter for non-equilibrium generalized spin models on honeycomb lattices

TL;DR

This paper introduces a new order-parameter for non-equilibrium spin models on honeycomb lattices that accounts for local environmental effects, providing insights into phase transitions and critical behavior.

Contribution

The paper proposes an alternative order-parameter considering local environmental influences, and analyzes its impact on phase diagrams and critical exponents in non-equilibrium spin models.

Findings

Stationary phase transition in the Ising universality class.

Estimated Wegner exponent as ω=1.06(9).

Finite-size corrections analyzed.

Abstract

An alternative definition for the order-parameter is proposed, for a family of non-equilibrium spin models with up-down symmetry on honeycomb lattices, and which depends on two parameters. In contrast to the usual definition, our proposal takes into account that each site of the lattice can be associated with a local temperature which depends on the local environment of each site. Using the generalised voter motel as a test case, we analyse the phase diagram and the critical exponents in the stationary state and compare the results of the standard order-parameter with the ones following from our new proposal, on the honeycomb lattice. The stationary phase transition is in the Ising universality class. Finite-size corrections are also studied and the Wegner exponent is estimated as $\omega=1.06(9)$.