Metastability region in spin-glasses

The stability of the Sherrington-Kirkpatrick model is reconsidered, pointing out that the de Almeida-Thouless line from the phase diagram does not imply the replica symmetry breaking at the zero magnetic field.     

ε-expansion calculations for spin-glasses

The critical properties of the spin-glass transition proposed by Edwards and Anderson are studied using the minimal subtraction method. The universal ratio of the second correction to scaling amplitude to the square of the first for the order parameter susceptibility χ₀ is calculated to first order in ε(ε=6?d). Comparison is made with Fisch and Harris' high temperature series analysis which incorporated Rudnick-Nelson-type corrections to scaling. Within the same formalism the critical exponents are calculated to second order in ε. They agree with the first order ε expansion of Harris, Lubensky and Chen.     

Anisotropic spin-glasses with broken replica symmetry

A simple mechanism of replica symmetry breaking for spin-glass, as suggested by Parisi, has been used to solve the anisotropic spin-glass model of Sherrington and Ghatak. Temperature variation of the correlation parameters and the resulting variations with the temperature of the thermodynamic quantities like internal energy, specific heat and entropy have been evaluated. It is found that the anisotropy has considerable effect on the properties of the spin system. At low temperatures, the specific heat varies asT ². However, the entropy is positive for temperatures above 0.1°K, which is a considerable improvement on the results of Sherrington and Ghatak. The results are expected to be in good agreement with experiment or computer simulation studies near transition temperatures.     

Magnetic phase diagram of spinel spin-glasses

The article by Villain [Z. Phys. B — Condensed Matter33, 31 (1979)] is discussed and a modified magnetic phase diagram is suggested for the spinel system (AB₂O₄) in which theA andB sites are partially (or completely) occupied by magnetic atoms. This diagram takes into account the antiferromagnetic exchange interactionsJ _AA,J _BB andJ _AB between nearest neighbor cations of various types. Regions of paramagnetic, antiferromagnetic, ferrimagnetic and possible spin glass behaviour are indicated on the diagram.Supported by the National Science Foundation under Grant ISP-80-11451     

On the critical dynamics of spin-glasses

The dynamic scaling of the spin-glass model, proposed by Edwards and Anderson, is studied. The dynamic critical exponents are calculated at the freezing point and at the tricritical point. The coupling of the order parameter with propagating excitations is considered.     

Ultrametricity between states at different temperatures in spin-glasses

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-p-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized random-energy model. Received 18 March 2002 / Received in final form 14 June 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: tommaso.rizzo@inwind.it     

Coexistence of the itinerant-electron antiferromagnetism and the spin-glasses

The Born approximation has been used to calculate the phase diagram of the itinerant-electron antiferromagnet containing magnetic impurities in the spin-glass state.