stefan boettcher - emory universitystefan boettcher local field distributions in spin glasses...
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![Page 1: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/1.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses
APS-March Meeting
03-10-08
Collaborators:‣David Sherrington (Oxford U)‣Helmut Katzgraber (ETH Zürich)
Find in: arXiv:0711.3934 or JPA (soon)
1
![Page 2: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/2.jpg)
Local field distributions in spin glasses APS-March Meeting
03-10-08
Local field distributions in spin glasses
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Collaborators:‣David Sherrington (Oxford U)‣Helmut Katzgraber (ETH Zürich)
Find in: arXiv:0711.3934 or JPA (soon)
1
![Page 3: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/3.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Can Local Field Dist. P(h) distinguishbetween Spin Glass Models? ‣Low-d vs Mean-Field, ‣RS vs RSB,
‣Equilibrium vs Meta-Stable.
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![Page 4: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/4.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Can Local Field Dist. P(h) distinguishbetween Spin Glass Models? ‣Low-d vs Mean-Field, ‣RS vs RSB,
‣Equilibrium vs Meta-Stable.
⇒ Conclusions: ‣ All P(h) are amazingly similar,
‣ But: Characteristic variation near P(h=0)!
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![Page 5: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/5.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models:
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![Page 6: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/6.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;
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![Page 7: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/7.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;‣ 1d Long-Range Model, J ∝ r –σ;
3
![Page 8: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/8.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;‣ 1d Long-Range Model, J ∝ r –σ;
small large
σ
deff
rij
Jij =εij
rσij
3
![Page 9: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/9.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;‣ 1d Long-Range Model, J ∝ r –σ;
small large
σ
deff
rij
Jij =εij
rσij
large small
σ
deff
3
![Page 10: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/10.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;‣ 1d Long-Range Model, J ∝ r –σ;
small large
σ
deff
rij
Jij =εij
rσij
‣Sherrington-Kirkpatrick (SK), d→∞ or σ→0; large small
σ
deff
3
![Page 11: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/11.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;‣ 1d Long-Range Model, J ∝ r –σ;
small large
σ
deff
rij
Jij =εij
rσij
Methods:
‣Extremal Optimization Heuristic (T=0) for SK and EA;
‣Sherrington-Kirkpatrick (SK), d→∞ or σ→0; large small
σ
deff
3
![Page 12: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/12.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Models: ‣Edwards-Anderson (EA) for d=2,3,4;‣ 1d Long-Range Model, J ∝ r –σ;
small large
σ
deff
rij
Jij =εij
rσij
Methods:
‣Extremal Optimization Heuristic (T=0) for SK and EA;‣Parallel Tempering (T=0.05...1.4) for Long-Range Model;
‣Sherrington-Kirkpatrick (SK), d→∞ or σ→0; large small
σ
deff
3
![Page 13: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/13.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Sherrington-Kirkpatrick:
4
![Page 14: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/14.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
slop
e ~0
.3Sherrington-Kirkpatrick:
4
![Page 15: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/15.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
slop
e ~0
.3Sherrington-Kirkpatrick:
4
![Page 16: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/16.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
slop
e ~0
.3Sherrington-Kirkpatrick:
4
![Page 17: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/17.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
slop
e ~0
.3
P(h=0)~0.15/√N
Sherrington-Kirkpatrick:
4
![Page 18: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/18.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Sherrington-Kirkpatrick: sl
ope
~0.3
P(h=0)→0
Edwards-Anderson:
5
![Page 19: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/19.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Sherrington-Kirkpatrick: sl
ope
~0.3
P(h=0)→0
Edwards-Anderson:
5
![Page 20: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/20.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-08
Sherrington-Kirkpatrick: sl
ope
~0.3
P(h=0)→0
Edwards-Anderson:
⇒ in EA:‣ Slope ∼0.23..0.25‣ P(0)>0, but small!
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![Page 21: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/21.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
6
![Page 22: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/22.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
6
![Page 23: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/23.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
⇒ in SK:‣ Slope ∼0.3,‣ P(0)→0,
⇒ in EA:‣ Slope ∼0.23,‣ P(0)>0,
⇒ in 1d LR:‣ Slope ∼0.3,‣ P(0)>0,
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![Page 24: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/24.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
7
![Page 25: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/25.jpg)
Fixed Size N , varying σ or d :
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
7
![Page 26: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/26.jpg)
Fixed Size N , varying σ or d :
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
7
![Page 27: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/27.jpg)
Fixed Size N , varying σ or d :
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
7
![Page 28: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/28.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson:
8
![Page 29: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/29.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson: P(0) for varying σ or d :
8
![Page 30: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/30.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson: sl
ope
P(0) for varying σ or d :
8
![Page 31: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/31.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson: sl
ope
P(0) for varying σ or d :
8
![Page 32: Stefan Boettcher - Emory UniversityStefan Boettcher Local field distributions in spin glasses APS-March Meeting 03-10-08 Can Local Field Dist. P(h) distinguish](https://reader036.vdocument.in/reader036/viewer/2022070115/60ada4ff31a694055d594fcf/html5/thumbnails/32.jpg)
StefanBoettcherwww.physics.emory.edu/faculty/boettcher/
Local field distributions in spin glasses APS-March Meeting
03-10-081d Long-Range: Edwards-Anderson: sl
ope
Connectivity: 2d=N-1
P(0) for varying σ or d :
8