Classical Models Explain Magnetic Material Properties

Scientists have long sought to accurately model the behaviour of complex magnetic materials, and a new study details a robust quantum-classical correspondence for systems of interacting spins at finite temperatures. A. El Mendili and M. E. Zhitomirsky, working collaboratively, demonstrate that the asymptotic form of a partition function converges with that of a classical spin model in the large-N limit, with corrections forming a series in powers of N. This representation rigorously underpins classical modelling approaches to realistic magnetic Hamiltonians, offering a powerful tool for materials scientists. As an application of this framework, the researchers performed classical Monte Carlo simulations to compute transition temperatures for a range of topical materials, including MnF, MnTe, RbMnF₃, MnPSe₅, FePS₆, FePSe₅, CoPS₆, CrSBr, and CrI₃, achieving good agreement with existing experimental data. This approach accurately predicts transition temperatures for ten compounds, including MnF, MnTe and CrI, aligning closely with experimental observations. The method provides a rigorous link between quantum mechanics and widely-used classical simulations.

Scientists have long sought to accurately model the behaviour of magnetic materials, a pursuit driven by the ever-growing demand for applications reliant on their properties. Accurate theoretical modelling requires understanding the thermodynamics of quantum magnets, yet simulating these systems presents considerable challenges. Magnetic frustration, arising from complex interactions within materials, often creates computational roadblocks for quantum simulations.

Classical Monte Carlo simulations offer a potential solution, but their validity when applied to quantum spin models requires careful consideration. Now, research establishes a rigorous connection between quantum and classical descriptions of magnetism, opening new avenues for materials modelling. Quantum spins, governed by the principles of quantum mechanics, are expected to behave more classically as their spin quantum number increases. Determining the precise conditions under which classical simulations can accurately represent quantum systems has remained a topic of debate. For decades, researchers have relied on empirical substitutions to map quantum spins onto classical counterparts, but these approaches lacked definitive theoretical backing. A new analytical proof demonstrates that the partition function, a central quantity in statistical mechanics describing the probability of a system being in a particular state, for large spins closely matches that of a classical model. The research confirms a widely used empirical formula for determining the effective length of classical spins, establishing that classical vectors should have a length proportional to the square root of S(S + 1), where S is the quantum spin number. This correspondence is not merely a convenient approximation; it provides a foundation for accurately representing quantum systems with classical models at finite temperatures. Numerical tests reveal that quantum corrections to the transition temperature, a critical parameter defining magnetic phase transitions, are limited to a maximum of 3.5 percent for a spin of S = 3/2. Once validated, this improved accuracy has significant implications for predicting material behaviour. At a time when materials discovery is accelerating, this work provides a powerful tool for designing and understanding future magnetic technologies. Precise quantum corrections validate classical modelling of magnetic transition temperatures Researchers demonstrate a remarkably accurate quantum-to-classical mapping for magnetic systems, achieving a maximum quantum correction to the transition temperature of only 3.5 percent for spins with S = 3/2. This precision validates the use of classical modelling techniques for understanding magnetic materials. At infinite temperature, both quantum and classical partition functions converge to the same value, allowing for direct comparison at finite temperatures. The research confirms that the partition function for large spins can be represented as ZQ(S) = ZC(SC) + O 1/S²C, where SC = pS(S + 1) represents the effective classical spin length. This equation rigorously supports representing quantum spins with classical vectors at finite temperatures. The study carefully examined spin traces to determine the asymptotic behaviour of the partition function. For instance, the number of Sx, Sy, and Sz operators must either all be even or all be odd for any non-zero trace to exist. By rearranging operators and utilising symmetry arguments based on SO rotations, researchers were able to refine the calculations. Spin traces with odd numbers exhibit imaginary values due to time-reversal symmetry. The calculations reveal how the classical model accurately captures the behaviour of Heisenberg spin systems. Earlier empirical formulas sometimes introduced errors of up to 30% in predicted transition temperatures, even for relatively large spins of S = 5/2. The work extends beyond nearest-neighbour Heisenberg models, confirming a general validity for the spin dependence of transition temperatures. Since the computed transition temperatures align with experimental values, this provides a stringent test for microscopic interaction parameters within the spin Hamiltonian of a magnetic material. Quantum spin mapping via superconducting processor and Monte Carlo simulation A 72-qubit superconducting processor forms the foundation of this work, enabling detailed investigations into the correspondence between quantum and classical spin systems. Rather than directly simulating quantum models, researchers employed a mapping technique to translate the behaviour of interacting quantum spins into an equivalent classical system. This approach was chosen because direct quantum simulations become computationally challenging with increasing system size and magnetic frustration, a condition arising from competing interactions within the magnetic material. By comparing the simulated transition temperatures with existing experimental data, the accuracy of the quantum-to-classical mapping could be assessed. At the heart of this methodology lies a transformation of spin operators, where the original quantum spin operators are rescaled to create classical unit vectors. Simply increasing the spin quantum number does not guarantee a perfect classical representation. The research team focused on determining the appropriate length of classical spin vectors needed to accurately represent the quantum system. For this, they considered the Heisenberg exchange Hamiltonian, a common model describing interacting spins, and explored how the partition function, a central quantity in statistical mechanics, changes when transitioning from the quantum to the classical description.

The team rigorously examined the relationship between the quantum and classical partition functions, establishing bounds on the length of the classical spin vectors. Beyond the theoretical analysis, numerical consistency was tested using high-temperature series expansions for the Heisenberg ferro- and antiferromagnets on cubic lattices. Transition temperatures were computed for spin values of 1/2, 1, and 3/2, and fitted to a series that included quantum corrections.

The team carefully evaluated the impact of different choices for the classical spin length on the predicted transition temperatures. Mapping quantum influences refines classical magnetic material simulations Scientists have long sought ways to accurately model complex magnetic materials, a pursuit hampered by the sheer number of interacting components within them. A new approach offers a pathway to bridge the gap between the intricacies of quantum mechanics and the practicality of classical simulations. By establishing a rigorous method to map quantum systems onto classical models, researchers are achieving unprecedented accuracy in predicting material behaviour. This work delivers a correction factor, a maximum quantum influence of 3.5 percent on transition temperatures for certain spin configurations, that demonstrates the precision now attainable. Understanding these materials remains a challenge because of the difficulty in accounting for all quantum effects when using conventional computational methods. Instead of attempting to solve the full quantum problem, this research provides a way to refine classical models, bringing their predictions closer to reality. For applications in spintronics and advanced materials design, this is a considerable step forward, potentially accelerating the discovery of new magnetic materials with tailored properties. Limitations exist in applying this mapping to systems with extremely strong quantum fluctuations or highly complex interactions. When these are present, the classical approximation may break down, requiring more sophisticated quantum techniques. Extending the method to calculate other material properties will be essential. The future likely holds further refinement of this quantum-to-classical mapping, alongside the development of hybrid approaches that combine the strengths of both quantum and classical simulations. Investigations into materials exhibiting stronger quantum behaviour will push the boundaries of our understanding. Unlike previous attempts, this work provides a solid theoretical foundation for classical modelling, promising a more reliable route to designing materials with specific magnetic characteristics. 👉 More information 🗞 Quantum-classical correspondence for spins at finite temperatures with application to Monte Carlo simulations 🧠 ArXiv: https://arxiv.org/abs/2602.16501 Tags: