1,721,320 research outputs found
The Mean Field Theory of Spin Glasses: The Heuristic Replica Approach and Recent Rigorous Results
No full textThe mathematically correct computation of the spin glasses free energy in the infinite range limit crowns 25 years of mathematic efforts in solving this model. The exact solution of the model was found many years ago by using a heuristic approach; the results coming from the heuristic approach were crucial in deriving the mathematical results. The mathematical tools used in the rigorous approach are quite different from those of the heuristic approach. In this note we will review the heuristic approach to spin glasses in the light of the rigorous results; we will also discuss some conjectures that may be useful to derive the solution of the model in an alternative way
Some considerations of finite-dimensional spin glasses
No full textIn this paper I will review the theoretical results that have been obtained for spin glasses, paying particular attention to finite-dimensional spin glasses. I will concentrate my attention on the formulation of the mean-field approach and on its numerical and experimental verifications. I will mainly consider equilibrium properties at zero magnetic field, where the situation is clear and it should not be controversial. I will present the various hypotheses on the basis of the theory and I will discuss their physical status
Low-temperature glassy systems: Present understanding, open problems and future developments
No full textOn the most compact regular lattices in large dimensions: A statistical mechanical approach
No full textIn this paper I will consider the computation of the maximum density of regular lattices in large dimensions using an approach based on statistical mechanics. The starting point will be some theorems of Rogers, which are virtually unknown in the community of physicists. Using his approach one can find many similarities (and differences) with the problem of computing the entropy of a system of hard spheres. The relation between the two problems is investigated in detail. Some conjectures are presented: further investigation is needed in order to check their consistency
Spin glass theory: Numerical and experimental results in three-dimensional systems
No full textHere I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental verifications. © 2007 Elsevier B.V. All rights reserved
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