Exact solution of the Ising model on group lattices of genus g>1

DOI10.1063/1.531690zbMath0862.20031arXivcond-mat/9603072OpenAlexW1970824455WikidataQ61444483 ScholiaQ61444483MaRDI QIDQ5284243

Riccardo Zecchina, Tullio Regge

Publication date: 26 May 1997

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

Full work available at URL: https://arxiv.org/abs/cond-mat/9603072

zbMATH Keywords

signsweightsIsing modelspartition functionsgroup extensionsPfaffianstopological genusgroup latticesKlein lattice group

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Other groups related to topology or analysis (20F38) Applications of linear algebraic groups to the sciences (20G45)

Related Items (8)

Dimer problem for some three dimensional lattice graphs ⋮ Belief propagation and loop series on planar graphs ⋮ Differential geometry of group lattices ⋮ Towards a theory of frustrated degeneracy. ⋮ ABSENCE OF SPONTANEOUS MAGNETIZATION FOR THE ISING MODEL ON WEAKLY SEPARABLE GRAPHS ⋮ Dimers and the critical Ising model on lattices of genus \(>1\) ⋮ Fermions and loops on graphs: II. A monomer–dimer model as a series of determinants ⋮ Computation of sparse circulant permanents via determinants

Cites Work

• Statistical mechanics models and the modular group
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

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