We study the recently introduced SWAP ensemble for Ising spin-glasses, where the spins obtain varying lengths, with length scale $Δ\in [0, 2]$ . The lengths can be exchanged in the spirit of the SWAP algorithm for glassy poly-disperse hard-sphere systems. Using an annealing schedule, if the annealing is slow enough, ground states of the corresponding Ising Hamiltonian, where the spin lengths are incorporated into the bonds, can be obtained with high probability. We prove this statement for two-dimensional systems with sizes of up to $L^2=1024^2$ spins by comparison with exact ground states obtained by using graph matching algorithms. In particular, we analyze the nature of the obtained realizations of the disorder by calculating exact zero-temperature domain-wall energies, from exact ground state calculations using periodic and anti-periodic boundary conditions. For medium or large values of $Δ$ , e.g. $Δ=1$ , the realizations turn ferromagnetic if the annealing is slow enough, i.e., they lose their zero-temperature spin-glass property. If $Δ$ is small, the realizations remain glassy, but the SWAP annealing does not easily find a true ground state.We study the recently introduced SWAP ensemble for Ising spin-glasses, where the spins obtain varying lengths, with length scale $Δ\in [0, 2]$. The lengths can be exchanged in the spirit of the SWAP algorithm for glassy poly-disperse hard-sphere systems. Using an annealing schedule, if the annealing is slow enough, ground states of the corresponding Ising Hamiltonian, where the spin lengths are incorporated into the bonds, can be obtained with high probability. We prove this statement for two-dimensional systems with sizes of up to $L^2=1024^2$ spins by comparison with exact ground states obtained by using graph matching algorithms. In particular, we analyze the nature of the obtained realizations of the disorder by calculating exact zero-temperature domain-wall energies, from exact ground state calculations using periodic and anti-periodic boundary conditions. For medium or large values of $Δ$, e.g. $Δ=1$, the realizations turn ferromagnetic if the annealing is slow enough, i.e., they lose their zero-temperature spin-glass property. If $Δ$ is small, the realizations remain glassy, but the SWAP annealing does not easily find a true ground state.

arXiv:2610.05046Oct 4, 20260 citations

Matching Kasteleyn cities for spin glass ground states

Creighton K. Thomas, A. Alan Middleton

As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and applied to two-dimensional Ising spin glasses. The algorithm combines the Pfaffian and matching approaches to directly strip droplet excitations from an excited state. Extended ground states in Ising spin glasses on a torus, which are optimized over all boundary conditions, are used to compute precise values for ground state energy densities.As spin glass materials have extremely slow dynamics, devious numerical methods are needed to study low-temperature states. A simple and fast optimization version of the classical Kasteleyn treatment of the Ising model is described and applied to two-dimensional Ising spin glasses. The algorithm combines the Pfaffian and matching approaches to directly strip droplet excitations from an excited state. Extended ground states in Ising spin glasses on a torus, which are optimized over all boundary conditions, are used to compute precise values for ground state energy densities.

arXiv:0706.2866Physical Review BDec 17, 200741 citations

Numerical and experimental studies of the dynamics of Ising spin glasses

Jan‐Olov Andersson

Jan 1, 19941 citation

Sampling the ground-state magnetization of d -dimensional p -body Ising models

Creighton K. Thomas, Helmut G. Katzgraber

We demonstrate that a recently introduced heuristic optimization algorithm [Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic crossover genetic updates is capable of sampling nearly uniformly among ground-state configurations in spin-glass-like Hamiltonians with $p$ -spin interactions in $d$ space dimensions that have highly degenerate ground states. Using this algorithm we probe the zero-temperature ferromagnet to spin-glass transition point ${q}_{c}$ of two example models, the disordered version of the two-dimensional three-spin Baxter-Wu model [ ${q}_{c}=0.1072(1)$ ] and the three-dimensional Edwards-Anderson model [ ${q}_{c}=0.2253(7)$ ], by computing the Binder ratio of the ground-state magnetization.We demonstrate that a recently introduced heuristic optimization algorithm [Phys. Rev. E 83, 046709 (2011)] that combines a local search with triadic crossover genetic updates is capable of sampling nearly uniformly among ground-state configurations in spin-glass-like Hamiltonians with $p$-spin interactions in $d$ space dimensions that have highly degenerate ground states. Using this algorithm we probe the zero-temperature ferromagnet to spin-glass transition point ${q}_{c}$ of two example models, the disordered version of the two-dimensional three-spin Baxter-Wu model [${q}_{c}=0.1072(1)$] and the three-dimensional Edwards-Anderson model [${q}_{c}=0.2253(7)$], by computing the Binder ratio of the ground-state magnetization.

arXiv:1108.1953Physical Review BNov 4, 20116 citations

Comparative monte Carlo study of ising spin glasses in two to five dimensions

Dietrich Stauffer, Kurt Binder

The European Physical Journal BMar 1, 197925 citations

We study the recently introduced SWAP ensemble for Ising spin-glasses, where the spins obtain varying lengths, with length scale

Δ\in [0, 2]

. The lengths can be exchanged in the spirit of the SWAP algorithm for glassy poly-disperse hard-sphere systems. Using an annealing schedule, if the annealing is slow enough, ground states of the corresponding Ising Hamiltonian, where the spin lengths are incorporated into the bonds, can be obtained with high probability. We prove this statement for two-dimensional systems with sizes of up to

L^2=1024^2

spins by comparison with exact ground states obtained by using graph matching algorithms. In particular, we analyze the nature of the obtained realizations of the disorder by calculating exact zero-temperature domain-wall energies, from exact ground state calculations using periodic and anti-periodic boundary conditions. For medium or large values of

Δ

, e.g.

Δ=1

, the realizations turn ferromagnetic if the annealing is slow enough, i.e., they lose their zero-temperature spin-glass property. If

Δ

is small, the realizations remain glassy, but the SWAP annealing does not easily find a true ground state.

p

-spin interactions in

d

space dimensions that have highly degenerate ground states. Using this algorithm we probe the zero-temperature ferromagnet to spin-glass transition point

{q}_{c}

of two example models, the disordered version of the two-dimensional three-spin Baxter-Wu model [

{q}_{c}=0.1072(1)

] and the three-dimensional Edwards-Anderson model [

{q}_{c}=0.2253(7)

], by computing the Binder ratio of the ground-state magnetization.