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

Marek Semjan,Milan Žukovič,Gh Adam,M Hnatič,J Buša

doi:10.1051/epjconf/202022602019

Marek Semjan, Milan Žukovič + Show 3 more

Open Access

https://doi.org/10.1051/epjconf/202022602019

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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 for the 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 the easier to implement TIM can yield results of comparable accuracy with that of the more involved WL method.

Highlights

Calculation of global thermodynamic properties, which cannot be measured in Monte Carlo (MC) simulation directly, such as the free energy and the entropy, is generally a difficult task
We compare the performance of the WL and thermodynamic integration method (TIM) methods for the calculation of the global thermodynamic quantities of a highly frustrated Ising antiferromagnet on a Kagome lattice (IAKL) [6] with the focus on the entropy, the ground-state value of which is exactly known [7]
IAKL is a typical example of a complex spin system with high geometrical frustration resulting in a massive ground-state degeneracy with a finite residual entropy and no long-range ordering at any temperature

Summary

Introduction

Calculation of global thermodynamic properties, which cannot be measured in Monte Carlo (MC) simulation directly, such as the free energy and the entropy, is generally a difficult task. The exponential increase of the configurational space with the system size N makes this approach intractable even for moderate sizes and small number of degrees of freedom, such as the Ising model with the configuration space increasing as 2N. Since its introduction in 1977, it has been sparingly used, even though several studies pointed to its competitiveness [4, 5], for example in calculation of the ground-state entropy of some typical disordered/frustrated spin systems, such as the ±J Ising model and the spin-s triangular lattice Ising antiferromagnet. We compare the performance of the WL and TIM methods for the calculation of the global thermodynamic quantities of a highly frustrated Ising antiferromagnet on a Kagome lattice (IAKL) [6] with the focus on the entropy, the ground-state value of which is exactly known [7]

Model and methods

MA and TIM

WL algorithm

Results and discussion