Infinite Volume Limit and Spontaneous Replica Symmetry Breaking in Mean Field Spin Glass Models

2003 ◽  
Vol 4 (S1) ◽  
pp. 441-444 ◽  
Author(s):  
Francesco Guerra ◽  
Fabio Lucio Toninelli
Keyword(s):  
Symmetry Breaking ◽  
Spin Glass ◽  
Mean Field ◽  
Infinite Volume ◽  
Replica Symmetry ◽  
Replica Symmetry Breaking ◽  
Volume Limit ◽  
Infinite Volume Limit

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

scholarly journals Excitation Spectrum of Interacting Bosons in the Mean-Field Infinite-Volume Limit

2014 ◽  
Vol 15 (12) ◽  
pp. 2409-2439 ◽  
Author(s):  
Jan Dereziński ◽  
Marcin Napiórkowski
Keyword(s):  
Excitation Spectrum ◽  
Mean Field ◽  
Infinite Volume ◽  
Volume Limit ◽  
The Mean ◽  
Infinite Volume Limit
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