Nov 11, 2022

The mathematics that makes us realize we don’t know much: Behavior of spin glasses

Posted by in categories: economics, mathematics, physics, robotics/AI

Spin glasses are alloys formed by noble metals in which a small amount of iron is dissolved. Although they do not exist in nature and have few applications, they have nevertheless been the focus of interest of statistical physicists for some 50 years. Studies of spin glasses were crucial for Giorgio Parisi’s 2021 Nobel Prize in Physics.

The scientific interest of spin glasses lies in the fact that they are an example of a complex system whose elements interact with each other in a way that is sometimes cooperative and sometimes adversarial. The mathematics developed to understand their behavior can be applied to problems arising in a variety of disciplines, from ecology to machine learning, not to mention economics.

Spin glasses are , that is, systems in which individual elements, the spins, behave like small magnets. Their peculiarity is the co-presence of ferromagnetic-type bonds, which tend to align the spins, with antiferromagnetic-type bonds, which tend to orient them in opposite directions.

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