Spin and link overlaps in 3-dimensional spin glasses

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 nontrivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically nontrivial 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 nontrivial spin overlap distribution P(q). These low energy excitations are not domain-wall-like, rather they are topologically nontrivial 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."

arXiv:cond-mat/0002055Physical Review LettersOct 2, 2000153 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

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

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

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

Low temperature behaviour of 3-D spin glasses in a magnetic field

Sergio Caracciolo A, Giorgio Parisi A, Stefano Patarnello +1 more

We present the results of two sets of numerical simulations of 3-d Ising spin-glasses in the presence of an uniform magnetic field. In the first set, among other quantities, we compute the spin-spin overlap probability distribution P (q ), the link-link overlap probability distribution P e(qe) and the spin-glass susceptibility χ SG for different volumes and temperatures. The results are in good agreement with mean-field behaviour : P(q) and P e(qe) are non trivial and non self-averaging and χSG shows an increase with the linear size L of the system as χSG ∼ Lω. Our estimate is ω = 1,8 ± 0.25 at T = 0.83. In the second set of simulations a small coupling ε is introduced between two copies of the system and the copy overlap Q(ε) is computed as a function of ε. Q(ε) becomes steeper around ε ∼ 0 as L increases, in agreement with the previous set of simulations. Our data seem anyhow incompatible with the alternatives to mean-field theory proposed so far.We present the results of two sets of numerical simulations of 3-d Ising spin-glasses in the presence of an uniform magnetic field. In the first set, among other quantities, we compute the spin-spin overlap probability distribution P (q ), the link-link overlap probability distribution P e(qe) and the spin-glass susceptibility χ SG for different volumes and temperatures. The results are in good agreement with mean-field behaviour : P(q) and P e(qe) are non trivial and non self-averaging and χSG shows an increase with the linear size L of the system as χSG ∼ Lω. Our estimate is ω = 1,8 ± 0.25 at T = 0.83. In the second set of simulations a small coupling ε is introduced between two copies of the system and the copy overlap Q(ε) is computed as a function of ε. Q(ε) becomes steeper around ε ∼ 0 as L increases, in agreement with the previous set of simulations. Our data seem anyhow incompatible with the alternatives to mean-field theory proposed so far.

Journal de physiqueJan 1, 199055 citations

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 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.