We present a collection of simulations of the Edwards–Anderson lattice spin glass at T=0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses.We present a collection of simulations of the Edwards–Anderson lattice spin glass at T=0 to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample the ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a variety of accurate exponents for domain wall stiffness and finite-size corrections, which allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattice Ising spin glasses.

arXiv:2407.14646Frontiers in PhysicsSep 20, 20242 citations

Phase transitions in spin glasses

A. P. Young

Journal of Magnetism and Magnetic MaterialsNov 21, 20064 citations

Low-temperature phase boundary of dilute-lattice spin glasses

Stefan Boettcher, Emiliano Marchetti

The thermal-to-percolative crossover exponent $\ensuremath{\phi}$, well known for ferromagnetic systems, is studied extensively for Edwards--Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold ${p}_{c}$ using an improved reduction algorithm. Simulations extend to system sizes above $N={10}^{8}$ in dimensions $d=2,\dots{},7$ . The results can be related to the behavior of the transition temperature ${T}_{g}\ensuremath{\sim}{(p\ensuremath{-}{p}_{c})}^{\ensuremath{\phi}}$ between the paramagnetic and the glassy regime for $p\ensuremath{\searrow}{p}_{c}$. In three dimensions, where our simulations predict $\ensuremath{\phi}=1.127(5)$, this scaling form for ${T}_{g}$ provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimensions near and above the upper critical dimension, the results provide a challenge to reconcile mean-field theory with finite-dimensional properties.The thermal-to-percolative crossover exponent $\ensuremath{\phi}$, well known for ferromagnetic systems, is studied extensively for Edwards--Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold ${p}_{c}$ using an improved reduction algorithm. Simulations extend to system sizes above $N={10}^{8}$ in dimensions $d=2,\dots{},7$. The results can be related to the behavior of the transition temperature ${T}_{g}\ensuremath{\sim}{(p\ensuremath{-}{p}_{c})}^{\ensuremath{\phi}}$ between the paramagnetic and the glassy regime for $p\ensuremath{\searrow}{p}_{c}$. In three dimensions, where our simulations predict $\ensuremath{\phi}=1.127(5)$, this scaling form for ${T}_{g}$ provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimensions near and above the upper critical dimension, the results provide a challenge to reconcile mean-field theory with finite-dimensional properties.

Physical Review BMar 27, 20083 citations

{p}_{c}

using an improved reduction algorithm. Simulations extend to system sizes above

N={10}^{8}

in dimensions

d=2,\dots{},7

. The results can be related to the behavior of the transition temperature ${T}_{g}\ensuremath{\sim}{(p\ensuremath{-}{p}_{c})}^{\ensuremath{\phi}}$ between the paramagnetic and the glassy regime for $p\ensuremath{\searrow}{p}_{c}$. In three dimensions, where our simulations predict $\ensuremath{\phi}=1.127(5)$, this scaling form for

{T}_{g}

provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimensions near and above the upper critical dimension, the results provide a challenge to reconcile mean-field theory with finite-dimensional properties.