The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the real axis in the thermodynamic limit. However, in frustrated systems such as antiferromagnets and spin glasses, the zeros deviate from this structure, making it challenging to extend the Lee-Yang theory to disordered systems. In this work, we establish a new circle theorem for two-dimensional Ising spin glasses, proving that the square of the partition function exhibits zeros densely packed along the unit circle. Numerical simulations on the square lattice confirm our theoretical predictions, demonstrating the validity of the circle law for quenched disorder. Furthermore, our results uncover a finite-temperature crossover in $\pm J$ spin glasses, characterized by the emergence of a spectral gap in the angular distribution of zeros. This result extends the Lee-Yang framework to disordered systems, offering new insights into spin-glass criticality.The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the real axis in the thermodynamic limit. However, in frustrated systems such as antiferromagnets and spin glasses, the zeros deviate from this structure, making it challenging to extend the Lee-Yang theory to disordered systems. In this work, we establish a new circle theorem for two-dimensional Ising spin glasses, proving that the square of the partition function exhibits zeros densely packed along the unit circle. Numerical simulations on the square lattice confirm our theoretical predictions, demonstrating the validity of the circle law for quenched disorder. Furthermore, our results uncover a finite-temperature crossover in $\pm J$ spin glasses, characterized by the emergence of a spectral gap in the angular distribution of zeros. This result extends the Lee-Yang framework to disordered systems, offering new insights into spin-glass criticality.

arXiv:2503.09876Mar 12, 20250 citations

Low-temperature renormalisation group for disordered ferromagnets and spin glasses

Gary S. Grest

Disordered spin systems with the number of spin components m are studied in dimensions d=2+ epsilon for small epsilon . For dilute quenched random systems, it is found that the system has the same critical behaviour as for a pure ferromagnetic if m>2. For the spin-glass phase, new critical exponents are calculated for m>or=2. The x-y spin glass is found to have a phase, new critical exponents are calculated for m>or=2. The x-y spin glass is found to have a vanishing critical temperature as d approaches 2, in contrast to the ferromagnetic x-y model.Disordered spin systems with the number of spin components m are studied in dimensions d=2+ epsilon for small epsilon . For dilute quenched random systems, it is found that the system has the same critical behaviour as for a pure ferromagnetic if m>2. For the spin-glass phase, new critical exponents are calculated for m>or=2. The x-y spin glass is found to have a phase, new critical exponents are calculated for m>or=2. The x-y spin glass is found to have a vanishing critical temperature as d approaches 2, in contrast to the ferromagnetic x-y model.

Journal of Physics C Solid State PhysicsNov 28, 19775 citations

Disordered Quantum Solids

Thierry Giamarchi, E. Orignac

Springer eBooksJan 1, 20012 citations

Disordered Quantum Solids

Thierry Giamarchi, E. Orignac

Springer eBooksMay 8, 20060 citations

\pm J

spin glasses, characterized by the emergence of a spectral gap in the angular distribution of zeros. This result extends the Lee-Yang framework to disordered systems, offering new insights into spin-glass criticality.