Introduction to mean-field theory of spin glass models

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68378271%3A_____%2F15%3A00456231" target="_blank" >RIV/68378271:_____/15:00456231 - isvavai.cz</a>
Result on the web
—
DOI - Digital Object Identifier
—

Result language
angličtina
Original language name
Introduction to mean-field theory of spin glass models
Original language description
We discuss the mean-field theory of spin-glass models with frustrated long-range random spin exchange. We analyze the reasons for breakdown of the simple mean-field theory of Sherrington and Kirkpatrick. We relate the replica-symmetry breaking to ergodicity breaking and use the concept of real replicas to restore thermodynamic homogeneity of the equilibrium free energy in a replicated phase space. Embedded replications of the spin variables result in a set of hierarchical free energies and overlap susceptibilities between replica hierarchies as order parameters. The limit to infinite number of replica hierarchies leads to the Parisi solution with a continuous replica-symmetry breaking. We demonstrate the construction of the spin-glass mean-field solutions via real replicas on three spin-glass models: Ising, Potts and p-spin. An asymptotic expansion in each model is used to demonstrate various types of the transition from the paramagnetic to the glassy phase.
Czech name
—
Czech description
—

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)