Hyperscaling in the Domany-Kinzel Cellular Automaton

TL;DR

This paper investigates the apparent violation of hyperscaling in the Domany-Kinzel cellular automaton's critical endpoint, revealing that the order parameter's discontinuity explains the anomaly and proposing a new hyperscaling relation.

Contribution

It introduces a hyperscaling relation applicable to transitions with discontinuous order parameters, resolving previous inconsistencies in the Domany-Kinzel automaton.

Findings

Discontinuous order parameter at the critical endpoint explains hyperscaling violation

Derived a new hyperscaling relation for such transitions

Discussed applications to related cellular automata models

Abstract

An apparent violation of hyperscaling at the endpoint of the critical line in the Domany-Kinzel stochastic cellular automaton finds an elementary resolution upon noting that the order parameter is discontinuous at this point. We derive a hyperscaling relation for such transitions and discuss applications to related examples.