Complexity and Dynamics of Spin Glass Systems

Spin glasses are paradigmatic examples of disordered and frustrated systems in which magnetic moments, or “spins”, interact through random couplings that can be either ferromagnetic or antiferromagnetic. This competition gives rise to a highly non‐trivial energy landscape with an exponentially large number of metastable states separated by energy barriers of varying heights. As a result, these materials exhibit slow, non‐equilibrium dynamics, characterised by history‐dependence, memory effects and ageing. The theoretical description has relied on mean-field models such as the Sherrington–Kirkpatrick Hamiltonian, replica methods, and numerical simulations. These approaches have revealed intricate organisational principles, including hierarchical state structures and replica symmetry breaking. Beyond condensed-matter physics, spin-glass ideas have found broad application in optimisation theory, neural networks, statistical inference and combinatorial problems, where rugged landscapes and slow dynamics pose fundamental challenges for algorithms and for understanding glassy transitions at a theoretical level.

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Complexity and Dynamics of Spin Glass Systems publication trend

The graph below shows the total number of articles in complexity and dynamics of spin glass systems across all publications each year (not limited to Nature Index journals).

Technical terms

Spin glass: A disordered magnetic system in which randomly assigned ferromagnetic and antiferromagnetic interactions lead to frustration and the absence of simple long-range order.

Energy landscape: The multidimensional surface defined by a system’s energy as a function of microscopic configurations, often punctuated by numerous local minima.

Replica symmetry breaking: A theoretical framework in which multiple identical representations of a system bifurcate into a hierarchy of distinct thermodynamic states to capture complex free‐energy structures.

Ageing: The slow evolution of dynamical response functions in glassy systems, in which relaxation times grow with the time elapsed since the system was prepared.

Overlap: A quantitative measure of similarity between two configurations in a disordered system, used to characterise clustering of states and ergodicity breaking.

References

1. Unlearnable Games and “Satisficing” Decisions: A Simple Model for a Complex World. Physical Review X (2024).
2. Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism. SciPost Physics (2024).
3. Complex Energy Landscapes in Spiked-Tensor and Simple Glassy Models: Ruggedness, Arrangements of Local Minima, and Phase Transitions. Physical Review X (2019).