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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis.
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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Scalable Multitemperature Free Energy Sampling of Classical Ising Spin States.

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We developed a discrete flow matching model for sampling material systems with discrete variables like atom types. This method efficiently samples free energy surfaces across temperatures and scales to larger systems, offering a low-cost solution.

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Area of Science:

  • Computational Materials Science
  • Statistical Physics
  • Machine Learning

Background:

  • Generative models excel at sampling continuous variables in materials but struggle with discrete variables.
  • Discrete variables like atom types or spin states are crucial in many material systems.
  • Existing methods for discrete systems are often computationally expensive or lack scalability.

Purpose of the Study:

  • To introduce a novel discrete flow matching model for systems with discrete phase-space coordinates.
  • To enable efficient and scalable free energy surface sampling across a wide temperature range.
  • To demonstrate the model's applicability to discrete systems like the 2D Ising model.

Main Methods:

  • Developed a discrete flow matching model tailored for discrete variables.
  • Applied the model to sample free energy surfaces of the 2D Ising model.
  • Evaluated the model's efficiency, reliability, and scalability.

Main Results:

  • The discrete flow matching model efficiently samples free energy surfaces over a wide temperature range.
  • The model generation is scalable to lattice sizes larger than the training set.
  • Demonstrated reliable free energy sampling on the 2D Ising model.

Conclusions:

  • Flow matching offers a low-cost and scalable approach for free energy sampling in discrete systems.
  • The developed model shows potential for applications in crystalline materials, including alchemical free energy calculations.
  • The codebase is publicly available, facilitating further research and development.