Markov chains for the analysis of states of one-dimensional spin systems

TL;DR

This paper models frustrated states of a one-dimensional dilute Ising chain using Markov chains, revealing how different chain types influence long-range order, entropy, and correlation length, especially under magnetic fields.

Contribution

It introduces a novel Markov chain classification for frustrated phases in the dilute Ising chain, linking chain type to physical properties and magnetic field effects.

Findings

Periodic chains exhibit long-range order and residual entropy.

Aperiodic chains lack long-range order with finite correlation length.

Magnetic field induces transitions between chain types.

Abstract

We analyze frustrated states of the one-dimensional dilute Ising chain with charged interacting impurities of two types with mapping of the system to some Markov chain. We perform classification and reveal two types of Markov chains: periodic with period 2 and aperiodic. Frustrated phases with various types of chains have different properties. In phases with periodic Markov chains, long-range order is observed in the sublattice while another sublattice remains disordered. This results in a conjunction of the non-zero residual entropy and the infinite correlation length. In frustrated phases with aperiodic chains, there is no long-range order, and the correlation length remains finite. It is shown that under the magnetic field the most significant change in the spin chain structure corresponds to the change of the Markov chain type.