Parisi’s Theory of Spin Glass

2021 ◽  
Vol 30 (12) ◽  
pp. 16-20
Author(s):  
Chulan KWON
Keyword(s):  
Spin Glass ◽  
Mean Field Theory ◽  
Mean Field ◽  
Exchange Interactions ◽  
The Novel ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Spin Glass Phase ◽  
Pure States ◽  
Novel Concept

The spin-glass phase is characterized by the existence of many pure states due to random exchange interactions between spins. Parisi established the novel concept of replica symmetry breaking (RSB) from Sherrington Kirkpatrick’s mean-field theory via an abstract replica trick. In this article, his RSB scheme is reviewed from the view point of infinitely many pure states.

The Infinite-Range Spin Glass

2013 ◽  
Author(s):  
Daniel L. Stein ◽  
Charles M. Newman
Keyword(s):  
Symmetry Breaking ◽  
Spin Glass ◽  
Spin Glasses ◽  
Mean Field Theory ◽  
Mean Field ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Glass Model ◽  
Kirkpatrick Model ◽  
Technical Details

This chapter introduces mean field theory, both as a general class of models and in its specific incarnation in spin glasses, the Sherrington–Kirkpatrick model. This is undoubtedly the most theoretically studied spin glass model by far, and the best understood. For the nonphysicist the going may get a little heavy in this chapter once replica symmetry breaking is introduced, with its attendant features of many states, non-self-averaging, and ultrametricity—but an attempt is made to define and explain what all of these things mean and why replica symmetry breaking represents such a radical departure from more conventional and familiar modes of symmetry breaking. While this is a central part of the story of spin glasses proper, the nonphysicist who wants to skip the technical details can safely omit certain sections in the chapter and continue on without losing the essential thread of the discussion that follows.

scholarly journals Replica symmetry breaking and the nature of the spin glass phase

1984 ◽  
Vol 45 (5) ◽  
pp. 843-854 ◽  
Author(s):  
M. Mézard ◽  
G. Parisi ◽  
N. Sourlas ◽  
G. Toulouse ◽  
M. Virasoro
Keyword(s):  
Symmetry Breaking ◽  
Spin Glass ◽  
Glass Phase ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Spin Glass Phase
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