System of 2 Derrida's models with fixed correlation between the spin configurations of subsystems

TL;DR

This paper investigates a combined system of two Derrida models with a fixed correlation constraint between their spin configurations, analyzing free energy and finite size effects using the Random Energy Model approach.

Contribution

It introduces a novel analysis of two Derrida models with fixed spin configuration correlation, extending the understanding of their joint behavior.

Findings

Derived free energy expressions for the coupled Derrida models.

Quantified finite size effects under fixed correlation constraints.

Provided insights into the energy landscape of correlated Derrida systems.

Abstract

The free energy and finite size effects are calculated for the system of 2 Derrida's models with fixed constraint between the spin configurations. Calculation were performed for the Random Energy Model approach.