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Information: the negative reciprocal value of probability.

                               Claude Shannon

An expert is a man who has made all the mistakes, which can be made, in a very narrow field.

                                                                Niels Bohr

18h
comment Percolation and number of phases in the 2D Ising model
See related question here.
19h
comment Percolation and number of phases in the 2D Ising model
@Velenik I lack sufficient ability to handle the basic concepts to understand for myself the typical arguments of publications on statistical mechanics and especially on the Ising model. But I think I'll get the maturity that much hope in this area.
19h
comment Percolation and number of phases in the 2D Ising model
@Velenik I will dedicate myself the next few weeks to chapter 6 of this book. I was very focused in the chapter on the Ising model. It is a very friendly text to a student. I believe this book will be a great reference in statistical mechanics. More and more I have good surprises with this book. I imagine that in the future will appear in the book, a section or chapter devoted to entropy and variational principles. I look forward to it.
19h
comment Percolation and number of phases in the 2D Ising model
@Velenik It is much simpler than I thought. The result is set forth in equation (6.22) of the book (update on April 1). It is a direct consequence of the DLR equations and almost certain uniqueness of conditional probability. I was very excited about the motivations given to set the DLR equations. Especially with the discussion of why the Kolmogorov's extension theorem does not solve the problem of the existence of Gibbs measure. Thank you very much.
1d
comment Percolation and number of phases in the 2D Ising model
By Gibbs measure in finite volume I want mean $\mu_{\Gamma}^\omega(A)=\sum_{\omega\in A}\frac{\exp\{\mathcal{H}_\Gamma^{-}(\omega)\}}{\mathcal{Z}_\Gamma^-}$ for all $A\in \{-1,+1\}^\Gamma$ and $\Gamma\subset \mathbb{Z}^2$. Here $\mathcal{H}_\Gamma^{-}(\omega)\}$ is the Hamiltonian.
1d
comment Percolation and number of phases in the 2D Ising model
@Velenik Dear Velenik, it occurred to me a question some time that resists my efforts to answer it for myself. I was reluctant to ask here but... The question is as follows. Given any $\nu\in\mathcal{G}$ and set $\omega_i=-1\forall i \in\mathbb{Z}^2 $ and $\mu_\Gamma^-(A)$ Gibbs measure in finite volume with boundary condition $-$. Is it true that $ \nu(\cdot|\mathcal{F}_{\Gamma^c})(\omega)=\nu(\cdot|\mathcal{F}_{\Gamma^c})(-)=\‌​mu_\Gamma^-(\cdot)$ This equality seems to me that was used tacitly in resolution up several times. For example the strong Markov property and stochastic monotonicity.
Mar
18
revised Percolation and number of phases in the 2D Ising model
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awarded  Autobiographer
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awarded  Curious
Apr
26
revised Phase transitions. Conceptual link of my intuitive notions and definition of Georgii's book in terms of probabilities
edited title
Apr
25
comment Ising model. What is large fluctuations of magnetization?
@YvanVelenik, Thank you. If my doubt is useful I will be happy to send it by email.
Apr
19
comment Ising model. What is large fluctuations of magnetization?
@hwlau Hello. Have some reference to this definition?
Apr
19
revised Ising model. What is large fluctuations of magnetization?
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Apr
19
revised Ising model. What is large fluctuations of magnetization?
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Apr
18
revised Ising model. What is large fluctuations of magnetization?
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Apr
18
revised Ising model. What is large fluctuations of magnetization?
added 74 characters in body
Apr
18
asked Ising model. What is large fluctuations of magnetization?
Dec
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revised Percolation and number of phases in the 2D Ising model
Add more instructive figure.
Oct
31
comment Percolation and number of phases in the 2D Ising model
Thank you Yvan Velenik! Just one last question. I believe now that I understand well the argument of the proof of this lemma. I can say that most of the lemas and propositions that follows this lema in the article in question depends upon the understanding this proof?
Oct
31
accepted Percolation and number of phases in the 2D Ising model