Cluster percolation and pseudocritical behavior in spin models

The critical behaviour of many spin models can be equivalently formulated as percolation of specific site-bond clusters. In the presence of an external magnetic field, such clusters remain well-defined and lead to a percolation transition, even though the system no longer shows thermal critical behaviour. We investigate the 2-dimensional Ising model and the 3-dimensional O(2) model by means of Monte Carlo simulations. We find for small fields that the line of percolation critical points has the same functional form as the line of thermal pseudocritical points.

Note:

11 pages, 7 figures, 2 tables, abstract partially changed, references added

model: spin
critical phenomena
cluster: percolation
magnetic field: external field
Ising model
symmetry: O(2)
dimension: 2
dimension: 3
lattice field theory
numerical calculations: Monte Carlo

References(17)

Figures(0)

Clusters and Ising critical droplets: a renormalization group approach

- J.Phys.A 13 (1980) 2775
•
DOI:
- 10.1088/0305-4470/13/8/025

Percolation and magnetization in the continuous spin Ising model

Piotr Bialas
(
- Bielefeld U. and
- Jagiellonian U.
)
,
Philippe Blanchard
(
- Bielefeld U.
)
,
Santo Fortunato
(
- Bielefeld U.
)
,
Daniel Gandolfo
(
- Bielefeld U. and
- Toulon U. and
- Marseille, CPT
)
,
Helmut Satz
(
- Bielefeld U.
)

- Nucl.Phys.B 583 (2000) 368-378
•
e-Print:
- hep-lat/0003014
•
DOI:
- 10.1016/S0550-3213(00)00332-1

Percolation and magnetization for generalized continuous spin models

Santo Fortunato
(
- Bielefeld U.
)
,
Helmut Satz
(
- Bielefeld U.
)

- Nucl.Phys.B 598 (2001) 601-611
•
e-Print:
- hep-lat/0007005
•
DOI:
- 10.1016/S0550-3213(01)00034-7

Cluster percolation in O(n) spin models

P. Blanchard
(
- Bielefeld U.
)
,
S. Digal
(
- Bielefeld U.
)
,
S. Fortunato
(
- Bielefeld U.
)
,
D. Gandolfo
(
- Sud Toulon Var U. and
- Marseille, CPT
)
,
T. Mendes
(
- Bielefeld U.
)

et al.

- J.Phys.A 33 (2000) 8603-8614
•
e-Print:
- hep-lat/0007035
•
DOI:
- 10.1088/0305-4470/33/48/301

- Physica A 161 58

- Physica A 175 222

Percolation and cluster distribution. 1. Cluster multiple labeling technique and critical concentration algorithm

J. Hoshen
(
- Michigan U.
)
,
R. Kopelman
(
- Michigan U.
)

- Phys.Rev.B 14 (1976) 3438-3445
•
DOI:
- 10.1103/PhysRevB.14.3438

Finite size effects, Goldstone bosons and critical exponents in the d = 3 Heisenberg model

- Nucl.Phys.B 350 (1991) 893-905
•
DOI:
- 10.1016/0550-3213(91)90167-V

A New Method for the Partition Function of Discrete Systems With Application to the 3- $d$ Ising Model

Gyan Bhanot
(
- Florida State U., SCRI
)
,
Steve Black
(
- Florida State U., SCRI
)
,
Paul Carter
(
- Florida State U., SCRI
)
,
Roman Salvador
(
- Florida State U., SCRI
)

- Phys.Lett.B 183 (1987) 331-336
•
DOI:
- 10.1016/0370-2693(87)90973-7

COMPLEX ZEROS IN THE PARTITION FUNCTION OF THE FOUR-DIMENSIONAL SU(2) LATTICE GAUGE MODEL

- Phys.Lett.B 108 (1982) 331-332
•
DOI:
- 10.1016/0370-2693(82)91205-9

Complex Zeros of the $d=3$ Ising Model: Finite Size Scaling and Critical Amplitudes

Enzo Marinari
(
- Saclay, SPhT
)

- Nucl.Phys.B 235 (1984) 123,
- IN *CARDY, J.L. (ED.): FINITE-SIZE SCALING* 312-323. (NUCL. PHYS. B235 |FS11| (1984) 123-134) AND SACLAY CEN - S.PH.T-83-142 (83,REC.DEC.) 20 P. (SEE BOOK INDEX)
•
DOI:
- 10.1016/0550-3213(84)90152-4

New Monte Carlo Technique for Studying Phase Transitions

- Phys.Rev.Lett. 61 (1988) 2635-2638
•
DOI:
- 10.1103/PhysRevLett.61.2635

Optimized Monte Carlo analysis

- Phys.Rev.Lett. 63 (1989) 1195-1198
•
DOI:
- 10.1103/PhysRevLett.63.1195

Collective Monte Carlo Updating for Spin Systems

Ulli Wolff
(
- Kiel U.
)

- Phys.Rev.Lett. 62 (1989) 361
•
DOI:
- 10.1103/PhysRevLett.62.361

High precision Monte Carlo study of the 3-D XY universality class

M. Hasenbusch
(
- Humboldt U., Berlin
)
,
T. Torok
(
- Humboldt U., Berlin
)

- J.Phys.A 32 (1999) 6361
•
e-Print:
- cond-mat/9904408
•
DOI:
- 10.1088/0305-4470/32/36/301

High precision Monte Carlo study of the 3-D XY universality class

M. Hasenbusch
(
- Humboldt U., Berlin
)
,
T. Torok
(
- Humboldt U., Berlin
)

- J.Phys.A 32 (1999) 6361
•
e-Print:
- cond-mat/9904408
•
DOI:
- 10.1088/0305-4470/32/36/301

A Numerical study of Goldstone mode effects and scaling functions of the three-dimensional O(2) model

- Nucl.Phys.B Proc.Suppl. 94 (2001) 861-864,
•
e-Print:
- hep-lat/0010004
•
DOI:
- 10.1016/S0920-5632(01)01020-9