Non-additive properties of finite 1D Ising chains with long-range interactions

TL;DR

This paper investigates the non-additive statistical properties of finite-range 1D Ising chains, focusing on mesoscopic fragments and deriving asymptotic expressions for energy and entropy in different interaction regimes.

Contribution

It introduces a novel analysis of non-additive properties in finite-range Ising chains using Markov sequence equivalence, providing new asymptotic formulas.

Findings

Derived asymptotic expressions for non-additive energy and entropy.

Analyzed variance of magnetization in mesoscopic fragments.

Explored effects of weak and strong interactions on statistical properties.

Abstract

We study the statistical properties of Ising spin chains with finite (although arbitrary large) range of interaction between the elements. We examine mesoscopic subsystems (fragments of an Ising chain) with the lengths comparable with the interaction range. The equivalence of the Ising chains and the multi-step Markov sequences is used for calculating different non-additive statistical quantities of a chain and its fragments. In particular, we study the variance of fluctuating magnetization of fragments, magnetization of the chain in the external magnetic field, etc. Asymptotical expressions for the non-additive energy and entropy of the mesoscopic fragments are derived in the limiting cases of weak and strong interactions.