Spin glasses with infinite-range and short-range interactions

1986 ◽  
Vol 58 (1-2) ◽  
pp. 117-122 ◽  
Author(s):  
K. Bien ◽  
K.D. Usadel
Keyword(s):  
Spin Glasses ◽  
Short Range ◽  
Infinite Range

DISTRIBUTION OF PURE STATES IN SHORT-RANGE SPIN GLASSES

2010 ◽  
Vol 24 (14) ◽  
pp. 2091-2106 ◽  
Author(s):  
C. M. NEWMAN ◽  
D. L. STEIN
Keyword(s):  
Spin Glasses ◽  
Short Range ◽  
Glass Phase ◽  
Single Pair ◽  
Mixed States ◽  
Spin Glass Phase ◽  
Kirkpatrick Model ◽  
Pure States ◽  
Mathematical Construct ◽  
Infinite Range

We review the structure of the spin glass phase in the infinite-range Sherrington–Kirkpatrick model and the short-range Edwards–Anderson (EA) model. While the former is now believed to be understood, the nature of the latter remains unresolved. However, considerable insight can be gained through the use of the metastate, a mathematical construct that provides a probability measure on the space of all thermodynamic states. Using tools provided by the metastate construct, possibilities for the nature of the organization of pure states in short-range spin glasses can be considerably narrowed. We review the concept of the "ordinary" metastate, and also newer ideas on the excitation metastate, which has been recently used to prove existence of only a single pair of ground states in the EA Ising model in the half-plane. We close by presenting a new result, using metastate methods, on the number of mixed states allowed in the EA model.

scholarly journals The state space of short-range Ising spin glasses: the density of states

1998 ◽  
Vol 2 (3) ◽  
pp. 313-317 ◽  
Author(s):  
T. Klotz ◽  
S. Schubert ◽  
K.H. Hoffmann
Keyword(s):  
State Space ◽  
Density Of States ◽  
Spin Glasses ◽  
Short Range ◽  
The State ◽  
Ising Spin

Ordered Phase of Short-Range Ising Spin-Glasses

1986 ◽  
Vol 56 (15) ◽  
pp. 1601-1604 ◽  
Author(s):  
Daniel S. Fisher ◽  
David A. Huse
Keyword(s):  
Spin Glasses ◽  
Short Range ◽  
Ising Spin

Ground-state properties of the infinite-range vector spin-glasses

1983 ◽  
Vol 28 (5) ◽  
pp. 2886-2889 ◽  
Author(s):  
Gary S. Grest ◽  
C. M. Soukoulis
Keyword(s):  
Ground State ◽  
Spin Glasses ◽  
Ground State Properties ◽  
Range Vector ◽  
Infinite Range

scholarly journals Correspondence between long-range and short-range spin glasses

2012 ◽  
Vol 86 (13) ◽  
Author(s):  
R. A. Baños ◽  
L. A. Fernandez ◽  
V. Martin-Mayor ◽  
A. P. Young
Keyword(s):  
Long Range ◽  
Spin Glasses ◽  
Short Range

scholarly journals Generic replica symmetric field-theory for short range Ising spin glasses

2002 ◽  
Vol 25 (3) ◽  
pp. 361-372 ◽  
Author(s):  
T. Temesvári ◽  
C. De Dominicis ◽  
I.R. Pimentel
Keyword(s):  
Field Theory ◽  
Spin Glasses ◽  
Short Range ◽  
Ising Spin ◽  
Symmetric Field
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