Thermodynamic properties of the ferrimagnetic spin chains in the presence of a magnetic field

TL;DR

This paper compares three methods—cumulant expansion, modified spin wave theory, and quantum Monte Carlo simulations—to analyze the thermodynamic properties of ferrimagnetic spin chains under magnetic fields, highlighting their respective strengths.

Contribution

It extends cumulant expansion to ferrimagnetic chains with magnetic fields and compares it with other methods for accurate thermodynamic analysis.

Findings

Cumulant expansion performs well at moderate and high temperatures.

Modified spin wave theory is accurate at low temperatures.

The methods' convergence regions overlap, making them complementary.

Abstract

We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic ($S=5/2, s=2$) spin chains. The application of cumulant expansion has been generalized to the ferrimagnetic chain in the presence of an external magnetic field. Using cumulants, we have obtained the field dependent effective Hamiltonian in terms of the classical variables up to the second order of quantum corrections. Thermodynamic functions, the internal energy, the specific heat and the magnetic susceptibility are obtained from the effective Hamiltonian. We have also examined the modified spin wave theory to derive the same physical properties. Finally, we have studied our model using quantum Monte Carlo simulation to obtain accurate results. The comparison of the above results and also the high temperature series expansion shows that cumulant expansion gives good results for moderate and high temperature regions while the modified spin wave theory is good for low temperatures. Moreover, the convergence regions of the cumulant expansion and the modified spin wave theory overlap each other which propose these two as a set of complement methods to get the thermodynamic properties of spin models.