Matching Kasteleyn Cities for Spin Glass Ground States

  title={Matching Kasteleyn Cities for Spin Glass Ground States},
  author={Creighton K. Thomas and A. Alan Middleton},
  journal={Physical Review B},
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… Expand

Figures from this paper

Exact ground states of large two-dimensional planar Ising spin glasses.
  • G. Pardella, F. Liers
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
This work presents an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction using Kasteleyn cities, and points out that the correctness of heuristically computed ground states can easily be verified. Expand
Ground States of Two-Dimensional Ising Spin Glasses: Fast Algorithms, Recent Developments and a Ferromagnet-Spin Glass Mixture
Using advanced numerical approaches based on optimization algorithms, much progress has been achieved for the study of the ground-state and low-temperature behavior of two-dimensional Ising spinExpand
A dedicated algorithm for calculating ground states for the triangular random bond Ising model
An algorithm for the computation of ground state spin configurations for the 2 d random bond Ising model on planar triangular lattice graphs is presented and the critical behavior of the corresponding T = 0 ferromagnet to spin-glass transition is investigated. Expand
High-precision studies of domain-wall properties in the 2D Gaussian Ising spin glass
In two dimensions, short-range spin glasses order only at zero temperature, where efficient combinatorial optimization techniques can be used to study these systems with high precision. The use ofExpand
Chaos in spin glasses revealed through thermal boundary conditions
Spin glasses have competing interactions that lead to a rough energy landscape which is highly susceptible to small perturbations. These chaotic effects strongly affect numerical simulations and, asExpand
Evidence against a mean-field description of short-range spin glasses revealed through thermal boundary conditions
A theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. In particular, it is unclear if theories that assert a single pair of pure states,Expand
Domain-wall excitations in the two-dimensional Ising spin glass
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-theoreticExpand
Universality in phase boundary slopes for spin glasses on self-dual lattices
We study the effects of disorder on the slope of the disorder–temperature phase boundary near the Onsager point (Tc = 2.269...) in spin-glass models. So far, studies have focused on marginal orExpand
From Spin Glasses to Negative-Weight Percolation
The question of whether NWP exhibits properties of Stochastic–Loewner Evolution is addressed and recent results for directed NWP are presented. Expand
Information-theoretic approach to ground-state phase transitions for two- and three-dimensional frustrated spin systems.
  • O. Melchert, A. Hartmann
  • Physics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
The information-theoretic observables entropy, excess entropy, and multi-information are used to analyze ground-state spin configurations for disordered and frustrated model systems in two and three dimensions to detect changes in the spatial structure of the ground states as the critical point is approached. Expand


Spin Glass Theory and Beyond
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particularExpand
New Optimization Algorithms in Physics
List of Contributors. 1 Introduction (A.K. Hartmann and H. Rieger). Part I: Applications in Physics. 2 Cluster Monte Carlo Algorithms (W. Krauth). 2.1 Detailed Balance and a priori Probabilities. 2.2Expand