1. A Multicanonical Monte Carlo Study of the 3D ±J Spin Glass
Naomichi Hatano*,**
James E. Gubernatis**
*Aoyama Gakuin University
**Los Alamos National Laboratory

2. H Â J s = - Â The ±J Model 1 q = s N ij i ( a ) j · , Ò 1 2 (quenched)
replica 1
Overlap Order Parameter q = 1 N s i ( ) 2 Â
replica 2

3. Low-Temperature Phase
Mean-field picture
(Parisi et al.)
Droplet picture
(Fisher & Huse)
L 
T ª 0

4. Order-Parameter Distribution

5. At higher temperatures

6. Flattening the histogram
Microcanonical: Few low-energy states
Canonical: Few high-energy states
Trapped by local minima
Multicanonical: Samples uniformly

7. Auto-Correlation Time
Making the bivariate histogram h(E,q) flat
Berg & Janke, PRL80, 4771 (‘98)
(*) Monovariate multicanonical
(*)

8. Monovariate Multicanonical

9. Density of States D(E,q)

10. Summary Monte Carlo Method  Correlation Time: N
Bivariate Multicanonical
Monte Carlo Method
 Correlation Time: N
Low-Temperature Phase
 The result of P(q; T=0.3)
suggests the droplet picture

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