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Tag: Ising spin glass

Visualizing Variables with the 2-D Cluster Variation Method

Visualizing Variables with the 2-D Cluster Variation Method

Cluster Variation Method – 2-D Case – Configuration Variables, Entropy and Free Energy Following the previous blog on the 1-D Cluster Variation Method, I illustrate here a micro-ensemble for the 2-D Cluster Variation Method, consisting of the original single zigzag chain of only ten units (see previous post), with three additional layers added, as shown in the following Figure 1. In Figure 1, we again have an equilibrium distribution of fraction variables z(i). Note that, as with the 1-D case,…

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Modeling Trends in Long-Term IT as a Phase Transition

Modeling Trends in Long-Term IT as a Phase Transition

The most reasonable model for our faster-than-exponential growth in long-term IT trends is that of a phase transition. At a second-order phase transition, the heat capacity becomes discontinuous. The heat capacity image is provided courtesy of a wikipedia site on heat capacity transition(s). L. Witthauer and M. Diertele present a number of excellent computations in graphical form in their paper The Phase Transition of the 2D-Ising Model. There is another interesting article by B. Derrida & D. Stauffer in Europhysics…

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Gibbs Free Energy, Belief Propagation, and Markov Random Fields

Gibbs Free Energy, Belief Propagation, and Markov Random Fields

Correspondence Between Free Energy, Belief Propagation, and Markov Random Field Models As a slight digression from previous posts – re-reading the paper by Yedidia et al. on this morning on Understanding Belief Propagation and its Generalizations – which explains the close connection between Belief Propagation (BP) methods and the Bethe approximation (a more generalized version of the simple bistate Ising model that I’ve been using) in statistical thermodynamics. The important point that Yedidia et al. make is that their work…

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What Makes a Metastable State Happen?

What Makes a Metastable State Happen?

Metastable States – the Meltdown Precursors I’ve just read a recent column by JL, one of the editors from Taipan Daily. He states, in his column “There Will Be Blood in Europe”: Stepping back a bit: What is so frightening right now, not just in Europe but China and America and Japan too, is the presence of fraud-fueled “Lehman 2.0” catalysts threatening to explode. One could say that the 2008 financial crisis was the mother of all wake-up calls. But…

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"What is X?" – Modeling the Meltdown

"What is X?" – Modeling the Meltdown

“What is X?” – Modeling the 2008-2009 Financial Systems Meltdown We’re about to start a detailed walkthrough of applying a “simple” statistical thermodynamic model to the Wall Street players in the 2007-2009 timeframe. The two kinds of information that I’ll be joining together for this will be a description of Wall Street dynamics, based largely on Chasing Goldman Sachs (see previous blogposts for link), and the two-state Ising thermodynamic model that I’ve been presenting over the past several posts. The…

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Modeling Nonlinear Phenomena

Modeling Nonlinear Phenomena

Modeling Nonlinear Phenomena – What is “X”? Many of us grew up hating word problems in algebra. (Some of us found them interesting, sometimes easy, and sometimes fun. We were the minority.) For most of us, even if we understood the mathematical formulas, there was a big “gap” in our understanding and intuition when it came to applying the formulas to some real-world situation. In the problem, we’d be given a set of statements, and then told to find “something.”…

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The Beauty of Phase Spaces

The Beauty of Phase Spaces

Phase Spaces: Mapping Complex Systems I’ve spent the day on cloud computing. Yes, there will be a course on it at GMU this Fall of 2010. And cloud computing is simply a technology; a means of getting stuff done. In and of itself, I think there are more exciting things in the world — such as phase spaces. One of the classic nonlinear systems is the Ising spin glass model. This system is composed of only two kind of particles;…

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"Origins of Wealth" – A (Multi-Part) Critical Review

"Origins of Wealth" – A (Multi-Part) Critical Review

Over the last few months, questions of not only wealth and finances, but the underpinnings of our entire financial structure, have become paramount in many of our minds. We — that usually means you and me — and right now means the world collectively — have largely misunderstood the world’s financial structure over recent years. (Those who HAVE accurately understood are not only more secure, but substantially richer by now.) Most of us are current on “what went wrong.” Most…

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