R Mélin et al 1996 J. Phys. A: Math. Gen. 29 5773 doi:10.1088/0305-4470/29/18/011
Glassy behaviour in the ferromagnetic Ising model on a Cayley tree
R Mélin
, J C Anglès d'Auriac, P Chandra
and B Douçot
We present a detailed study of the nearest-neighbour ferromagnetic Ising model on a Cayley tree. In the limit of zero field, the system displays glassy behaviour below a crossover temperature, 
, that scales inversely with the logarithm of the number of generations; thus is inversely proportional to the logarithm of the logarithm of the number of sites. Non-Gaussian magnetization distributions are observed for 
, reminiscent of that associated with the central spin of the Edwards - Anderson model on the same tree; furthermore, a dynamical study indicates metastability, long relaxation times and ageing consistent with the development of glassy behaviour for a finite but macroscopic number of sites.
- PACS
-
75.10.Hk Classical spin models
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
- MSC
-
82B30 Statistical thermodynamics (See also 80-XX)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
82B80 Numerical methods (Monte Carlo, series resummation, etc.) (See also 65-XX, 81T80)
- Subjects
- Dates
-
Issue 18 (21 September 1996)
Received 28 March 1996
-
Glassy behaviour in the ferromagnetic Ising model on a Cayley tree
R Mélin et al 1996 J. Phys. A: Math. Gen. 29 5773
-
Channel switching and magnetoresistance of a metal-SiO2-Si structure
J Dai et al 2000 J. Phys. D: Appl. Phys. 33 L65
-
Use of the discriminant Fourier-derived cepstrum with feature-level post-processing for surface electromyographic signal classification
Xinpu Chen et al 2009 Physiol. Meas. 30 1399
-
Mass-producible replication of highly hydrophobic surfaces from plant leaves
Seung-Mo Lee and Tai Hun Kwon 2006 Nanotechnology 17 3189
-
Geometric properties of two-dimensional O(n) loop configurations
Chengxiang Ding et al 2007 J. Phys. A: Math. Theor. 40 3305
-
Effect of Ca doping on microstructural and superconducting properties of DyBa2Cu3O7−δ/Caz (0 ≤ z ≤ 0.2) ceramics
J Y Laval and T S Orlova 2003 Supercond. Sci. Technol. 16 1139
-
Scaling solutions and geodesics in moduli space
J L P Karthauser and P M Saffin 2006 Class. Quantum Grav. 23 4615
-
Hubble Space Telescope Observations of the Draco Dwarf Spheroidal Galaxy
Carl J. Grillmair et al. 1998 The Astronomical Journal 115 144
-
Analysis of the periodicity of voltage versus applied flux curves of planar and three-dimensional SQUIDs in the presence of coupling inhomogeneity
R De Luca 2009 Supercond. Sci. Technol. 22 125010
-
Radiative lifetimes of Rydberg 6pns and 6pnd J = 1 states of Pb I obtained from multichannel quantum defect theory
Zhenwen Dai et al 2002 J. Phys. B: At. Mol. Opt. Phys. 35 3111
Related review articles
What's this?- The effective temperature
- Unconventional phase transitions in a constrained single polymer chain
- Universality of Wigner random matrices: a survey of recent results