Understanding complex systems through mathematics: Unraveling the mystery of spin glasses

Spin glasses: The math that makes us realise we don’t really know much

Alloys of noble metals are formed when a small amount iron is dissolved. They are not found in nature, and they have very few applications. However, statistical physicists have been interested in them for over 50 years. The studies of spin glasses played a crucial role in Giorgio Parisi winning the 2021 Nobel Prize in Physics.

The scientific value of spin glasses is that they represent a complex system in which the elements can interact in both a cooperative and adversarial manner. The mathematics used to study their behavior can be used to solve problems in many disciplines from ecology to machine-learning, and not to mention, economics.

Spin glasses are magnetic system, which means that the individual elements behave as 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.