Finite size corrections on the boundary between the spin-glass and the ferromagnetic phases of Derrida's model

TL;DR

This paper investigates finite size effects on the phase boundary between spin-glass and ferromagnetic states in Derrida's model, with implications for information theory channel capacity.

Contribution

It provides analytical calculations of finite size corrections to free energy and magnetization at the phase boundary in Derrida's model.

Findings

Finite size corrections to free energy and magnetization were derived.

The phase boundary behavior parallels the channel capacity in information theory.

Results enhance understanding of finite system effects in disordered magnetic models.

Abstract

The boundary line between the ferromagnetic and the spin-glass phases was investigated. Finite size corrections to the free energy and magnetization were calculated. The situation coincides with the case in the information theory, when the transmission rate equals to the capacity of channel.