Random field induced order in low dimension. I

DOI10.1007/s00220-014-1979-zzbMath1292.82003arXiv1208.3149OpenAlexW2964291479MaRDI QIDQ2452199

Nicholas Crawford

Publication date: 30 May 2014

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3149

zbMATH Keywords

\(XY\) modelmagnetic orderrandom external field

Mathematics Subject Classification ID

Random fields (60G60) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of magnetic materials (82D40)

Related Items (2)

Decimations for one- and two-dimensional Ising and rotator models. II. Continuous vs discrete symmetries ⋮ Uniqueness of gradient Gibbs measures with disorder

Cites Work

• On random field induced ordering in the classical \(XY\) model
• The ground state of the three-dimensional random-field Ising model
• Order by disorder, without order, in a two-dimensional spin system with \(O(2)\) symmetry
• Rounding effects of quenched randomness on first-order phase transitions
• Scaling limits in statistical mechanics and microstructures in continuum mechanics
• Gibbs-non-Gibbs properties for \(n\)-vector lattice and mean-field models
• Gibbsianness versus non-Gibbsianness of time-evolved planar rotor models
• Parabolic Harnack inequality and estimates of Markov chains on graphs
• Thermal fluctuations in some random field models.
• The hierarchical random field Ising model.
• Nonexistence of random gradient Gibbs measures in continuous interface models in \(d=2\)
• Loss and recovery of Gibbsianness for XY models in external fields
• Exact zero-temperature critical behaviour of the ferromagnet in the uniaxial random field

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