Exact relations between damage spreading and thermodynamic functions for the N-color Ashkin-Teller model

TL;DR

This paper derives exact relations between damage spreading quantities and thermodynamic functions for the N-color Ashkin-Teller model, enabling more efficient and accurate determination of critical exponents.

Contribution

It establishes exact relations valid for any ergodic dynamics in the ferromagnetic N-color Ashkin-Teller model, aiding numerical analysis.

Findings

Relations valid for any ergodic dynamics

Applicable to translational invariant lattices

Facilitates more accurate critical exponent determination

Abstract

Exact results are derived relating quantities computable by the so-called damage spreading method and thermodynamic functions for the N-color Ashkin-Teller model. The results are valid for any ergodic dynamics. Since we restrict our analysis to the ferromagnetic case the results are also valid for any translational invariant lattice. The derived relations should be used in order to determine numerically the N-color Ashkin-Teller critical exponents with better accuracy and less computational efforts than standard Monte Carlo simulations.