Global Thermodynamic Properties of Complex Spin Systems Calculated from Density of States and Indirectly by Thermodynamic Integration Method

TL;DR

This paper compares the Wang-Landau and thermodynamic integration methods for calculating the entropy of a frustrated Kagome lattice Ising antiferromagnet, finding TIM to be as accurate as WL despite being simpler to implement.

Contribution

The study demonstrates that thermodynamic integration can achieve accuracy comparable to Wang-Landau sampling for complex spin systems.

Findings

TIM provides accurate entropy estimates similar to WL.

TIM is simpler to implement than WL.

Both methods effectively handle high frustration in spin systems.

Abstract

Evaluation of global thermodynamic properties, such as the entropy or the free energy, of complex systems featuring a high degree of frustration or disorder is often desirable. Nevertheless, they cannot be measured directly in standard Monte Carlo simulation. Therefore, they are either evaluated indirectly from the directly measured quantities, for example by the thermodynamic integration method (TIM), or by applying more sophisticated simulation methods, such as the Wang-Landau (WL) algorithm, which can directly sample density of states. In the present investigation we compare the performance of the WL and TIM methods in terms of calculation of the entropy of an Ising antiferromagnetic system on a Kagome lattice - a typical example of a complex spin system with high geometrical frustration resulting in a non-zero residual entropy the value of which is exactly known. It is found that in terms of accuracy the implementationally simpler TIM can deliver results comparable with the more involved WL method.