-
1
-
-
0002014946
-
Translation invariance and instability of phase coexistence in the two dimensional Ising system
-
M. Aizenman, Translation invariance and instability of phase coexistence in the two dimensional Ising system. Commun. Math. Phys. 73:83 94 (1980).
-
(1980)
Commun. Math. Phys
, vol.73
, pp. 8394
-
-
Aizenman, M.1
-
3
-
-
0033447464
-
Group-invariant percolation on graphs
-
I. Benjamini, R. Lyons, Y. Peres, and O. Schramm, Group-invariant percolation on graphs, Geom. Func. Analysis 9:29-66 (1999).
-
(1999)
Geom. Func. Analysis
, vol.9
, pp. 29-66
-
-
Benjamini, I.1
Lyons, R.2
Peres, Y.3
Schramm, O.4
-
4
-
-
0002305414
-
Critical percolation on any non-amenable group has no infinite clusters
-
to appear
-
I. Benjamini, R. Lyons, Y. Peres, and O. Schramm, Critical percolation on any non-amenable group has no infinite clusters, Ann. Probab., to appear.
-
Ann. Probab.
-
-
Benjamini, I.1
Lyons, R.2
Peres, Y.3
Schramm, O.4
-
8
-
-
0000393829
-
Density and uniqueness in percolation
-
R. M. Burton and M. Keane, Density and uniqueness in percolation, Commun. Math. Phys. 121:501-505 (1989).
-
(1989)
Commun. Math. Phys.
, vol.121
, pp. 501-505
-
-
Burton, R.M.1
Keane, M.2
-
9
-
-
0001722765
-
Gibbs state describing coexistence of phases for a three-dimensional Ising model
-
R. L. Dobrushin, Gibbs state describing coexistence of phases for a three-dimensional Ising model, Theory Probab. Appl. 17:582 600 (1972).
-
(1972)
Theory Probab. Appl.
, vol.17
, pp. 582600
-
-
Dobrushin, R.L.1
-
11
-
-
33749860660
-
On the random cluster model. III. The simple random cluster model
-
C. M. Fortuin, On the random cluster model. III. The simple random cluster model. Physica 59:545-570 (1972).
-
(1972)
Physica
, vol.59
, pp. 545-570
-
-
Fortuin, C.M.1
-
12
-
-
0041855748
-
On the random cluster model. I. Introduction and relation to other models
-
C. M. Fortuin and P. W. Kasteleyn, On the random cluster model. I. Introduction and relation to other models, Physica 57:536-564 (1972).
-
(1972)
Physica
, vol.57
, pp. 536-564
-
-
Fortuin, C.M.1
Kasteleyn, P.W.2
-
13
-
-
0002160945
-
Equilibrium states of the Ising model in the two phase region
-
G. Gallavotti and S. Miracle-Sole, Equilibrium states of the Ising model in the two phase region, Phys. Rev. B 5:2555-2559 (1972).
-
(1972)
Phys. Rev. B
, vol.5
, pp. 2555-2559
-
-
Gallavotti, G.1
Miracle-Sole, S.2
-
14
-
-
21344436631
-
The stochastic random-cluster process and the uniqueness of random-cluster measures
-
G. R. Grimmett, The stochastic random-cluster process and the uniqueness of random-cluster measures, Ann. Probab. 23:1461-1510 (1995).
-
(1995)
Ann. Probab.
, vol.23
, pp. 1461-1510
-
-
Grimmett, G.R.1
-
15
-
-
0000042426
-
Percolation in cursive Greek chi + 1 dimensions
-
G. R. Grimmett and D. J. A. Welsh, eds. Clarendon Press, Oxford
-
G. R. Grimmett and C. M. Newman, Percolation in cursive Greek chi + 1 dimensions, in Disorder in Physical Systems, G. R. Grimmett and D. J. A. Welsh, eds. (Clarendon Press, Oxford, 1990), pp. 167-190.
-
(1990)
Disorder in Physical Systems
, pp. 167-190
-
-
Grimmett, G.R.1
Newman, C.M.2
-
16
-
-
0004335677
-
-
preprint
-
O. Häggström, J. Jonasson, and R. Lyons, Explicit isoperimetric constants, phase transitions in the random-cluster and Potts models, and Bernoullicity, preprint.
-
Explicit Isoperimetric Constants, Phase Transitions in the Random-cluster and Potts Models, and Bernoullicity
-
-
Häggström, O.1
Jonasson, J.2
Lyons, R.3
-
17
-
-
0038934720
-
Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously
-
O. Häggström and Y. Peres, Monotonicity of uniqueness for percolation on Cayley graphs: All infinite clusters are born simultaneously, Probab. Th. Rel. Fields 113:273-285 (1999).
-
(1999)
Probab. Th. Rel. Fields
, vol.113
, pp. 273-285
-
-
Häggström, O.1
Peres, Y.2
-
18
-
-
0001607313
-
On the absence of non-translation invariant Gibbs states for the two dimensional Ising model
-
Esztergom, J. Fritz, J. L. Lebowitz and D. Szsz, eds. Amsterdam, North-Holland
-
Y. Higuchi, On the absence of non-translation invariant Gibbs states for the two dimensional Ising model, in Random Fields (Esztergom, 1979), J. Fritz, J. L. Lebowitz and D. Szsz, eds. (Amsterdam, North-Holland, 1981). Vol. I, pp. 517-534.
-
(1979)
Random Fields
, vol.1
, pp. 517-534
-
-
Higuchi, Y.1
-
19
-
-
0033070870
-
The random cluster model on a general graph and a phase transition characterization of nonamenability
-
J. Jonasson. The random cluster model on a general graph and a phase transition characterization of nonamenability, Stoch. Proc. Appl. 79:335-354 (1999).
-
(1999)
Stoch. Proc. Appl.
, vol.79
, pp. 335-354
-
-
Jonasson, J.1
-
20
-
-
85034179015
-
Amenability and phase transition in the Ising model
-
to appear
-
J. Jonasson and J. Steif, Amenability and phase transition in the Ising model, J. Theor. Probab., to appear.
-
J. Theor. Probab.
-
-
Jonasson, J.1
Steif, J.2
-
22
-
-
0001446038
-
Coexistence of phases in Ising ferromagnets
-
J. L. Lebowitz, Coexistence of phases in Ising ferromagnets, J. Stat. Phys. 16:463-476 (1977).
-
(1977)
J. Stat. Phys.
, vol.16
, pp. 463-476
-
-
Lebowitz, J.L.1
-
23
-
-
0000688715
-
Random walks and the growth of groups
-
R. Lyons, Random walks and the growth of groups, C.R. Acad. Sci. Paris Sér. I Math. 320:1361-1366 (1995).
-
(1995)
C.R. Acad. Sci. Paris Sér. I Math.
, vol.320
, pp. 1361-1366
-
-
Lyons, R.1
-
25
-
-
85009909568
-
Indistinguishability of percolation clusters
-
to appear
-
R. Lyons and O. Schramm, Indistinguishability of percolation clusters, Ann. Probab., to appear.
-
Ann. Probab.
-
-
Lyons, R.1
Schramm, O.2
-
26
-
-
38249030408
-
Isoperimetric inequalities, growth, and the spectrum of graphs
-
B. Mohar, Isoperimetric inequalities, growth, and the spectrum of graphs. Linear Algebra Appl. 103:119-131 (1988).
-
(1988)
Linear Algebra Appl.
, vol.103
, pp. 119-131
-
-
Mohar, B.1
-
27
-
-
0001227786
-
Infinite clusters in percolation models
-
C. M. Newman and L. S. Schulman, Infinite clusters in percolation models, J. Stat. Phys. 26:613-628 (1981).
-
(1981)
J. Stat. Phys.
, vol.26
, pp. 613-628
-
-
Newman, C.M.1
Schulman, L.S.2
-
30
-
-
0033077109
-
Stability of infinite clusters in supercritical percolation
-
R. H. Schonmann, Stability of infinite clusters in supercritical percolation, Probab. Th. Rel. Fields 113:287-300 (1999).
-
(1999)
Probab. Th. Rel. Fields
, vol.113
, pp. 287-300
-
-
Schonmann, R.H.1
-
32
-
-
0002500545
-
Ising models on the Lobachevsky plane
-
C. M. Series and Y. G. Sinai, Ising models on the Lobachevsky plane. Commun. Math. Phys. 128:63-76 (1990).
-
(1990)
Commun. Math. Phys.
, vol.128
, pp. 63-76
-
-
Series, C.M.1
Sinai, Y.G.2
-
33
-
-
0039862319
-
Ising models on hyperbolic graphs
-
C. C. Wu, Ising models on hyperbolic graphs, J. Stat. Phys. 85:251-259 (1997).
-
(1997)
J. Stat. Phys.
, vol.85
, pp. 251-259
-
-
Wu, C.C.1
|