Spin Models on "Thin" Graphs

Spin model configurations on 2D random lattices (graphs) can be generated by the Feynman diagrams of various matrix models. The planar limit of such an NxN matrix model is given by taking N -> infinity. The opposite limit of N->1 ("thin" random graphs) is also of interest and is related to spin models on Bethe lattices and the mean field approach.  A second stay at Orsay in 1993-4 as a Marie Curie fellow offered the opportunity to work on this with a PhD student there, Jean-Philippe Kownacki, which continued on returning to Heriot-Watt with Petr Plechac and others.

• C. Baillie, D. Johnston and J-P. Kownacki, Ising Spins on Thin Graphs: Nucl. Phys. B432, 551-570, (1994)

• C. Baillie, W. Janke, D. Johnston and P. Plechac, Spin Glasses on Thin Graphs: Nucl. Phys. B450 [FS], 730-752, (1995)

• C. Baillie, N. Dorey, W. Janke and D. Johnston, The Villain Model on Thin Graphs: Phys. Lett. B369, 123-9, (1996)

• C. Baillie, D. Johnston, E. Marinari and C. Naitza, Dynamic Behavior of Spin Glasses on Quenched phi3 graphs: J. Phys. A29, 6683-6691, (1996)

• D. Johnston and P. Plechac, Potts Models on Feynman Diagrams: J. Phys. A30, 7349-7363, (1997)

• D. Johnston and P. Plechac, Equivalence of Ferromagnetic Spin Models on Trees and Random Graphs: J. Phys. A31 475-482, (1998)

• D. Johnston, The Yang Lee Edge Singularity on Feynman Diagrams: J. Phys. A31 5461-5469, (1998)

• D. Johnston, Thin Animals, J. Phys. A31 9405-9417, (1998)

• D. Johnston and P. Plechac, Vertex Models on Feynman Diagrams, Phys. Lett. A248 37-45, (1998)

• D. Johnston, A Potts/Ising Correspondence on thin graphs, J. Phys. A32 5029-5036, (1999)