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Glauber Dynamics
ising model
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Related Publications
(13)
The logarithmic sobolev inequality for discrete spin systems on a lattice
Mixing in Time and Space for Lattice Spin Systems: A Combinatorial View
Glauber Dynamics on Trees and Hyperbolic Graphs
Improved Bounds for Sampling Colorings
Heat kernels and spectral theory
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Lectures on Glauber Dynamics for Discrete Spin Models
Lectures on Glauber Dynamics for Discrete Spin Models,10.1007/9783540481157_2,Fabio Martinelli
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Lectures on Glauber Dynamics for Discrete Spin Models
(
Citations: 56
)
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Fabio Martinelli
These notes have been the subject of a course I gave in the summer 1997 for the school in
probability theory
in SaintFlour. I review in a selfcontained way the state of the art, sometimes providing new and simpler proofs of the most relevant results, of the theory of
Glauber dynamics
for classical lattice spin models of statistical mechanics. The material covers the dynamics in the one phase region, in the presence of boundary phase transitions, in the phase coexistence region for the two dimensional
Ising model
and in the socalled Griffiths phase for random Systems.
DOI:
10.1007/9783540481157_2
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Citation Context
(35)
...Supported by many experiments and studies in the theory of dynamical critical phenomena, physicists believe that the spectralgap of the continuoustime dynamics on lattices has the following critical slowing down behavior (e.g., [16,20,
25
,38]): At high temperatures ( β< β c) the inversegap is O(1), at the critical βc it is polynomial in the surfacearea and at low temperatures it is exponential in it. This is known for Z 2 except at ...
...This provides an estimate of the spectralgap of the singlesite dynamics in terms of those of the individual blocks and the blockdynamics chain itself (see [
25
])...
...This theorem appears in [
25
] in a more general setting, and following is its reformulation for the special case of Glauber dynamics for the Ising model on a finite graph with an arbitrary boundary condition...
Jian Ding
,
et al.
Mixing Time of Critical Ising Model on Trees is Polynomial in the Heig...
...[14,
17
] and the recent work on the cutoff phenomenon for the mean field Ising model [15])...
...greater than δ> 0) as can be seen via standard comparison techniques [
17
]...
Fabio Martinelli
,
et al.
On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Bounda...
...We use the following decomposition result of Lucier and Molloy [21], which is an application of the block dynamics technique (see, Proposition 3.4 in [
23
]) to the Glauber dynamics on the complete trees combined with Lemma 2 in Mossel and Sly [27]...
Prasad Tetali
,
et al.
Phase Transition for the Mixing Time of the Glauber Dynamics for Color...
...L is defined with boundarysource choice (M, S) = (∅, ∂ − Q ˜ L ). A standard property known as finite speed of propagation (see [
22
]) asserts that for a proper C ,i fa is chosen large enough for all t,...
N. Cancrini
,
et al.
Kinetically Constrained Lattice Gases
...[
17
]. Much recent work has been devoted to determining sufficient and ne cessary conditions for rapid convergence of Gibbs samplers...
...It is based on a combination of block dynamics, see e.g. [
17
], and path coupling, see e.g...
...Proposition 1 If τblock is the relaxation time of the block dynamics andτi is the maximum the relaxation time on Vi given any boundary condition fromG − {Vi} then by Proposition 3.4 of [
17
]...
...Applying Lemma 2 and 3 we get that the block dynamics satisfies τblock ≤ Ck. Then by Proposition 3.4 of [
17
] we have that...
...for sufficiently large C. Then by Proposition 3.4 of [
17
] we have that...
...the mixing time of the block dynamics is simply 1. By applying Proposition 3.4 of [
17
] we get that the relaxation time on T ′ is simply the maximum of the relaxation times on the blocks,...
... Then by Proposition 3.4 of [
17
] we have that the relaxation time of the Glauber dynamics on Vj is bounded by nC . �...
...The main results now follows easily using the block dynamics approach of Proposition 3.4 of [
17
]...
... Then by Proposition 3.4 of [
17
] we have that the relaxation time is O(nC...
Elchanan Mossel
,
et al.
Gibbs rapidly samples colorings of G(n, d/n)
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Citations
(56)
Strong spatial mixing of $4$colorings on binary trees
Qi Ge
,
Daniel Stefankovic
Published in 2011.
Mixing Time of Critical Ising Model on Trees is Polynomial in the Height
(
Citations: 7
)
Jian Ding
,
Eyal Lubetzky
,
Yuval Peres
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 295, no. 1, pp. 161207, 2010
"Zero" temperature stochastic 3D Ising model and dimer covering fluctuations: a first step towards interface mean curvature motion
(
Citations: 2
)
Pietro Caputo
,
Fabio Martinelli
,
Francois Simenhaus
,
Fabio Lucio Toninelli
Published in 2010.
On the Mixing Time of the 2D Stochastic Ising Model with “Plus” Boundary Conditions at Low Temperature
(
Citations: 3
)
Fabio Martinelli
,
Fabio Lucio Toninelli
Journal:
Communications in Mathematical Physics  COMMUN MATH PHYS
, vol. 296, no. 1, pp. 175213, 2010
Phase Transition for the Mixing Time of the Glauber Dynamics for Coloring Regular Trees
(
Citations: 4
)
Prasad Tetali
,
Juan Carlos Vera
,
Eric Vigoda
,
Linji Yang
Conference:
ACMSIAM Symposium on Discrete Algorithms  SODA
, pp. 16461656, 2010