Limit ofFerromagnetic Models on Graphs
- 14 August 2000
- journal article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 85 (7) , 1496-1499
- https://doi.org/10.1103/physrevlett.85.1496
Abstract
Thirty years ago, H. E. Stanley showed that an O(n) spin model on a lattice tends to a spherical model as n-->infinity. This means that at any temperature the corresponding free energies coincide. This fundamental result is no longer valid on more general discrete structures lacking in translation invariance, i.e., on graphs. However, only the singular parts of the free energies determine the critical behavior of the two statistical models. Here we show that for ferromagnetic models such singular parts still coincide even on graphs in the thermodynamic limit. This implies that the critical exponents of O(n) models on graphs for n-->infinity tend to the spherical ones and depend only on the graph spectral dimension.Keywords
This publication has 9 references indexed in Scilit:
- Spectral partitions on infinite graphsJournal of Physics A: General Physics, 2000
- Geometrical Universality in Vibrational DynamicsModern Physics Letters B, 1997
- DYNAMICAL DIMENSION SPLITTING ON FRACTALS: STRUCTURES WITH DIFFERENT DIFFUSIVE AND VIBRATIONAL SPECTRAL DIMENSIONSModern Physics Letters B, 1996
- Local vs Average Behavior on Inhomogeneous Structures: Recurrence on the Average and a Further Extension of Mermin-Wagner Theorem on GraphsPhysical Review Letters, 1996
- Universal Properties of Spectral DimensionPhysical Review Letters, 1996
- Phase transitions and random walks on graphs: A generalization of the Mermin-Wagner theorem to disordered lattices, fractals, and other discrete structuresPhysical Review Letters, 1992
- Quantum PhysicsPublished by Springer Nature ,1987
- Gaussian Field Theories on General Networks and the Spectral DimensionsProgress of Theoretical Physics Supplement, 1987
- Spherical Model as the Limit of Infinite Spin DimensionalityPhysical Review B, 1968