Spin Models on Thin Graphs

We discuss the utility of analytical and numerical investigation of spin models, in particular spin glasses, on ordinary ``thin'' random graphs (in effect Feynman diagrams) using methods borrowed from the ``fat'' graphs of two dimensional gravity. We highlight the similarity with Bethe lattice calculations and the advantages of the thin graph approach both analytically and numerically for investigating mean field results.Comment: Contribution to Parallel Session at Lattice95, 4 pages. Dodgy compressed ps file replaced with uuencoded LaTex original + ps figure

Spin Glasses on Thin Graphs

In a recent paper we found strong evidence from simulations that the Isingantiferromagnet on ``thin'' random graphs - Feynman diagrams - displayed amean-field spin glass transition. The intrinsic interest of considering such random graphs is that they give mean field results without long range interactions or the drawbacks, arising from boundary problems, of the Bethe lattice. In this paper we reprise the saddle point calculations for the Ising and Potts ferromagnet, antiferromagnet and spin glass on Feynman diagrams. We use standard results from bifurcation theory that enable us to treat an arbitrary number of replicas and any quenched bond distribution. We note the agreement between the ferromagnetic and spin glass transition temperatures thus calculated and those derived by analogy with the Bethe lattice, or in previous replica calculations. We then investigate numerically spin glasses with a plus or minus J bond distribution for the Ising and Q=3,4,10,50 state Potts models, paying particular attention to the independence of the spin glass transition from the fraction of positive and negative bonds in the Ising case and the qualitative form of the overlap distribution in all the models. The parallels with infinite range spin glass models in both the analytical calculations and simulations are pointed out.Comment: 13 pages of LaTex and 11 postscript figures bundled together with uufiles. Discussion of first order transitions for three or more replicas included and similarity to Ising replica magnet pointed out. Some additional reference

MAGNETIZATION OF AMORPHOUS MAGNETS

On a étudié l'influence de la température sur la distribution des moments magnétiques dans un matériau amorphe où les interactions d'échange et l'amplitude du moment magnétique à OK sont distribués au hasard. Deux cas limites sont analysés particulièrement ; l'un où les spins sont fixés l'autre où les interactions sont constantes. L'aimantation moyenne est représentée sur une figure. La largeur constante de la distribution d'aimantation peut être expliquée par l'existence des deux effets qui sont antagonistes.The temperature dependence of the distribution of the magnetic moment in an amorphous magnet, where the exchange interactions and the magnitude of the magnetic moment at O K are random variables, has been investigated. In particular, we considered the two-limiting cases, the one with the fixed spin and the other with the fixed interaction. The mean magnetization is also shown in a figure. The temperature-dependence of the width of the magnetization distribution shows an opposite tendency to each other. It is to be noted that the constant width observed in the experiment can be explained by the simultaneous existence of the both effect