Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become ``trivial\'\'.Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become ``trivial\'\'.

Jan 1, 20004 citations

Trivial link but non-trivial spin overlaps in 3-dimensional spin glasses

Florent Krząkała, Olivier Martin

Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become ``trivial''.Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an LxLxL lattice with an O(1) energy cost, confirming the mean field picture of a non-trivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically non-trivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as L increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become ``trivial''.

Feb 3, 20000 citations

Nontrivial link overlap distribution in three-dimensional Ising spin glasses

Guy Hed, Eytan Domany

We investigate the distributions of the link overlap, $P(Q)$ , in three-dimensional Ising spin glasses. We use clustering methodology to identify a set of pairs of states from different Gibbs states and calculate its contribution to $P(Q)$ . We find that the distribution over this set does not become trivial as the system size increases.We investigate the distributions of the link overlap, $P(Q)$, in three-dimensional Ising spin glasses. We use clustering methodology to identify a set of pairs of states from different Gibbs states and calculate its contribution to $P(Q)$. We find that the distribution over this set does not become trivial as the system size increases.

arXiv:cond-mat/0608535Physical Review BOct 23, 20075 citations

On the true low-energy excitations of the three-dimensional spin glass

Claudio Chilin, Enzo Marinari, Víctor Martín-Mayor +3 more

We study the low-energy excitations of the three dimensional spin glass through a large-scale Monte Carlo simulation on lattices up to $L=18$ . We find smooth extrapolations down to zero temperature, which, in the case of the energy and of the link overlap, can be directly -- and favourably -- compared with previous investigations featuring ground states (i.e., at zero temperature). The best fit for the fractal dimension of the excitations is provided by Replica-Symmetry Breaking theory, but we also consider the alternative TNT description. The $P(q)$ is found to verify the Parisi-Toulouse temperature scaling. Our data provides a spectacular confirmation of the overlap-equivalence hypothesis.We study the low-energy excitations of the three dimensional spin glass through a large-scale Monte Carlo simulation on lattices up to $L=18$. We find smooth extrapolations down to zero temperature, which, in the case of the energy and of the link overlap, can be directly -- and favourably -- compared with previous investigations featuring ground states (i.e., at zero temperature). The best fit for the fractal dimension of the excitations is provided by Replica-Symmetry Breaking theory, but we also consider the alternative TNT description. The $P(q)$ is found to verify the Parisi-Toulouse temperature scaling. Our data provides a spectacular confirmation of the overlap-equivalence hypothesis.

arXiv:2606.07197Jun 5, 20260 citations

Numerical simulations of Ising spin glasses with free boundary conditions: The role of droplet excitations and domain walls

Wenlong Wang

The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the spin overlap distribution functions of periodic and free boundary conditions using population annealing Monte Carlo. For system sizes up to about 1000 spins, spin glasses show nontrivial spin overlap distributions. Periodic boundary conditions may trap diffusive domain walls which can contribute to small spin overlaps, and the other contribution is the existence of low-energy droplet excitations within the system. We use free boundary conditions to minimize domain-wall effects, and show that low-energy droplet excitations are the major contribution to small overlaps in numerical simulations. Free boundary conditions has stronger finite-size effects, and is likely to have the same thermodynamic limit with periodic boundary conditions.The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the spin overlap distribution functions of periodic and free boundary conditions using population annealing Monte Carlo. For system sizes up to about 1000 spins, spin glasses show nontrivial spin overlap distributions. Periodic boundary conditions may trap diffusive domain walls which can contribute to small spin overlaps, and the other contribution is the existence of low-energy droplet excitations within the system. We use free boundary conditions to minimize domain-wall effects, and show that low-energy droplet excitations are the major contribution to small overlaps in numerical simulations. Free boundary conditions has stronger finite-size effects, and is likely to have the same thermodynamic limit with periodic boundary conditions.

arXiv:1610.07692Physical review. EMar 28, 20173 citations

Large-scale low-energy excitations in 3-d spin glasses - Replica symmetry breaking and characterization in position space

J. Houdayer, Florent Krząkała, Olivier Martin

We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified.We numerically extract large-scale excitations above the ground state in the 3-dimensional Edwards-Anderson spin glass with Gaussian couplings. We find that associated energies are O(1), in agreement with the mean field picture. Of further interest are the position-space properties of these excitations. First, our study of their topological properties show that the majority of the large-scale excitations are sponge-like. Second, when probing their geometrical properties, we find that the excitations coarsen when the system size is increased. We conclude that either finite size effects are very large even when the spin overlap q is close to zero, or the mean field picture of homogeneous excitations has to be modified.

arXiv:cond-mat/0009382Dec 1, 200015 citations

We investigate the distributions of the link overlap,

P(Q)

, in three-dimensional Ising spin glasses. We use clustering methodology to identify a set of pairs of states from different Gibbs states and calculate its contribution to

P(Q)

. We find that the distribution over this set does not become trivial as the system size increases.

We study the low-energy excitations of the three dimensional spin glass through a large-scale Monte Carlo simulation on lattices up to

L=18

. We find smooth extrapolations down to zero temperature, which, in the case of the energy and of the link overlap, can be directly -- and favourably -- compared with previous investigations featuring ground states (i.e., at zero temperature). The best fit for the fractal dimension of the excitations is provided by Replica-Symmetry Breaking theory, but we also consider the alternative TNT description. The

P(q)

is found to verify the Parisi-Toulouse temperature scaling. Our data provides a spectacular confirmation of the overlap-equivalence hypothesis.