Towards a theory of frustrated degeneracy.

DOI10.1016/S0012-365X(03)00043-8zbMath1089.82015OpenAlexW2012614440MaRDI QIDQ1408874

Martin Loebl, Jan Vondrák

Publication date: 25 September 2003

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(03)00043-8

zbMATH Keywords

Ising spin glassGround stateDegeneracyTransfer matrix method

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

Computational hardness of enumerating groundstates of the antiferromagnetic Ising model in triangulations ⋮ Stable degeneracies for Ising models ⋮ Non-degenerated ground states and low-degenerated excited states in the antiferromagnetic Ising model on triangulations ⋮ Antiferromagnetic Ising model in triangulations with applications to counting perfect matchings ⋮ Polynomial degeneracy for the first \(m\) energy levels of the antiferromagnetic Ising model

Cites Work

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• On the theory of Pfaffian orientations. II: \(T\)-joins, \(k\)-cuts, and duality of enumeration
• On the dimer problem and the Ising problem in finite \(3\)-dimensional lattices
• The statistics of dimers on a lattice
• Combinatorial and topological approach to the 3D Ising model
• Exact solution of the Ising model on group lattices of genus g>1
• A Combinatorial Solution of the Two-Dimensional Ising Model

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