Thermodynamic properties of the XX model in a chain with a period two and three coupling

TL;DR

This paper derives exact solutions for the energy spectrum of the XX spin chain with period-two and three couplings, analyzing thermodynamic properties like free energy, entropy, and specific heat under external magnetic fields.

Contribution

It provides analytical and numerical solutions for the XX model with periodic couplings, revealing how thermodynamic quantities behave at low temperatures under magnetic fields.

Findings

Entropy and specific heat vanish exponentially at low temperatures for certain magnetic field ranges.

Exact solutions for the energy spectrum are obtained for period-two and three couplings.

Thermodynamic functions depend explicitly on temperature and magnetic field, showing phase transition-like behavior.

Abstract

The exact solutions for the energy spectrum of the XX model with a periodic coupling and an external transverse magnetic field $h$ are obtained. The diagonalization procedure is discussed, and analytical and numerical solutions are given. Using the solutions for period-two coupling, the free energy, entropy, and specific heat are calculated as functions of temperature and applied transverse external magnetic field. Their expressions show that below a particular value $v$ and above a value $u$ of the magnetic field $|h|$, the entropy and the specific heat vanish exponentially in the low temperature limit.