Related papers: Fractal dimension of spin glasses interfaces in di…
We study domain walls in 2d Ising spin glasses in terms of a minimum-weight path problem. Using this approach, large systems can be treated exactly. Our focus is on the fractal dimension $d_f$ of domain walls, which describes via $<\ell…
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to anti-periodic in one spatial direction is studied using both the strong-disorder renormalization group and the greedy algorithm for the…
The fractal dimension of excitations in glassy systems gives information on the critical dimension at which the droplet picture of spin glasses changes to a description based on replica symmetry breaking where the interfaces are space…
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient…
We study directly the length of the domain walls (DW) obtained by comparing the ground states of the Edwards-Anderson spin glass model subject to periodic and antiperiodic boundary conditions. For the bimodal and Gaussian bond…
We study how the ground state of the two-dimensional Ising spin glass with Gaussian interactions in zero magnetic field changes on altering the boundary conditions. The probability that relative spin orientations change in a region far from…
Spin glass dynamics is a strong function of spatial dimensionality $D$. The lower critical dimension is close to 2.5, so that, in two dimensions, the condensation temperature $T_\text{g}=0$, and only fluctuations are present at finite…
We investigate the XY spin-glass model in two and three dimensions using the domain-wall renormalization-group method. The results for systems of linear sizes up to L=12 (2D) and L=8 (3D) strongly suggest that the lower critical dimension…
Exact ground states of two-dimensional Ising spin glasses with Gaussian and bimodal (+- J) distributions of the disorder are calculated using a ``matching'' algorithm, which allows large system sizes of up to N=480^2 spins to be…
Mean field spin glass models have undergone substantial mathematical development, but finite dimensional short range spin glasses remain much less understood. This paper proves several rigorous zero temperature signatures of glassy behavior…
An XY model with random phase shifts as a model for a superconducting glass is studied in two and three dimensions by a zero temperature domain wall renormalization group which allows one to follow the flows of both the coupling constant…
We study domain-wall excitations in two-dimensional random-bond Ising spin systems on a square lattice with side length L, subject to two different continuous disorder distributions. In both cases an adjustable parameter allows to tune the…
We present numerical evidence that the techniques of conformal field theory might be applicable to two-dimensional Ising spin glasses with Gaussian bond distributions. It is shown that certain domain wall distributions in one geometry can…
An efficient Monte Carlo method is extended to evaluate directly domain-wall free-energy for randomly frustrated spin systems. Using the method, critical phenomena of spin-glass phase transition is investigated in 4d +/-J Ising model under…
The chiral spin-glass Potts system with q=3 states is studied in d=2 and 3 spatial dimensions by renormalization-group theory and the global phase diagrams are calculated in temperature, chirality concentration p, and chirality-breaking…
The XY model with quenched random disorder is studied by a zero temperature domain wall renormalization group method in 2D and 3D. Instead of the usual phase representation we use the charge (vortex) representation to compute the domain…
Recent developments in study of two-dimensional spin glass models are reviewed in light of fractal nature of droplets at zero-temperature. Also presented are some new results including a new estimate of the stiffness exponent using a…
In this paper we study the phase diagram of the disordered Ising ferromagnet. Within the framework of the Gaussian variational approximation it is shown that in systems with a finite value of the disorder in dimensions D=4 and D < 4 the…
With the help of EXACT ground states obtained by a polynomial algorithm we compute the domain wall energy at zero-temperature for the bond-random and the site-random Ising spin glass model in two dimensions. We find that in both models the…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…