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Topic: Mean Field Theory

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	Mean field theory - Wikipedia, the free encyclopedia
		In field theory, the Hamiltonian may be expanded in terms of the magnitude of fluctuations around the mean of the field.
		Physically, this means a MFT system has no fluctuations, but this coincides with the idea that one is replacing all interactions with a "mean field".
		The formal basis for mean field theory is the Bogoliubov inequality.
	en.wikipedia.org /wiki/Mean_field_theory (890 words)

	Mean Field Theory
		The goal of this section is to introduce the so-called mean field theory (also known as self consistent field theory) and to illustrate the theory by applying it to the description of the Ising model.
		The main idea of the mean field theory is to focus on one particle and assume that the most important contribution to the interactions of such particle with its neighboring particles is determined by the mean field due to the neighboring particles.
		is the contribution to the mean field due to the nearest neighbors.
	xbeams.chem.yale.edu /~batista/vaa/node39.html (394 words)

	Mean field theory -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-09)
		A (additional info and facts about many-body system) many-body system with interactions is generally very difficult to solve exactly, except for extremely simple cases (Gaussian field theory, 1D (additional info and facts about Ising model) Ising model.) The great difficulty (e.g.
		This is the trivial term, which does not affect the (additional info and facts about partition function) partition function of the system.
		mean value of the spin and the dynamic fluctuation value.
	www.absoluteastronomy.com /encyclopedia/m/me/mean_field_theory.htm (892 words)

	Mean Field Theory and Coherent Structures for Vortex Dynamics on the Plane - Lim (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Mean Field Theory and Coherent Structures for Vortex Dynamics on the Plane - Lim (ResearchIndex)
		Mean Field Theory and Coherent Structures for Vortex Dynamics on the Plane (1999)
		C.C. Lim, Mean field theory and coherent structures for vortex dynamics on the plane, Phys.
	citeseer.ist.psu.edu /lim99mean.html (542 words)

	[Swarm-Modelling] Mean Field Theory
		I can't imagine ham-piece4000, which sits on the right top of the stew kettle communicating with kidney-bean399, which sits on the left bottom of the kettle.) A much better term than "soup", "mean field", "well-stirred", "well-mixed", or "panmictic" is "fully connnected".
		> > Panmictic and mean field approximations are only equivalent when the > effect of interactions with the other agents can > be replaced by the average effect, multiplied by the interaction > rate.
		A mean field approximation is really only valid when > > > the effect of all agents is equivalent to the sum (or average) of the > > > agents - pretty much when there is no complex emergence in the system.
	www.swarm.org /pipermail/modelling/2003-May/003419.html (537 words)

	ipedia.com: Mean Field Theory Article (Site not responding. Last check: 2007-10-09)
		Mean Field Theory A many-body system with interactions is generally very difficult to solve exactly, except for extremely simple cases The great difficulty is the treatment of combinatorics generated...
		The ease of solving MFT problems means that a lot of insight into the behavior of the system can be obtained at a relatively low cost.
		MFT is known under a great many names and guises, see also Bragg-Williams Approximation, Bethe Approximation, Landau Theory.
	www.ipedia.com /mean_field_theory.html (352 words)

	The BioEbook (Site not responding. Last check: 2007-10-09)
		In the first application of MFT in protein simulation, presented by Elber and Karplus [4], approximate mean-field treatment of protein-ligand dynamics enabled detailed studies to be made of the diffusion pathways of carbon monoxide through myoglobin.
		Koehl, P and Delarue, M. Application of a self consistent mean field theory to predict protein side-chain conformations and estimate their conformational entropy.
		Improvement of side-chain modeling in proteins with the self-consistent mean field theory method based on an analysis of the factors influencing prediction.
	hyper.stanford.edu /~koehl/BioEbook/scmf.php (1263 words)

	A Mean-Field Theory for Suspension Sedimentation with Vortices (Site not responding. Last check: 2007-10-09)
		The classical theory of Batchelor (1972) assumes a homogeneous spatial distribution to obtain the average particle sedimentation velocity.
		In his theory, the diverging volume integral of the Stokes force exerted by the particles on the fluid is made to converge in an ad hoc manner that may explain the significant deviation between the theoretical and observed velocities.
		We report a new theory that explicitly accounts for inhomogeneous distribution due to screening effects, the vortex instability, the finite variance for particle velocity and a new average sedimentation velocity that is in better agreement with experimental data.
	www.nd.edu /~iutam/ix3.html (457 words)

	[Swarm-Modelling] Mean Field Theory
		Panmictic and mean field approximations are only equivalent when the effect of interactions with the other agents can be replaced by the average effect, multiplied by the interaction rate.
		People using "mean field" to mean "panmictic" are mistaken, misleading and downright obfuscatory...
		A mean field approximation is really only valid when > > the effect of all agents is equivalent to the sum (or average) of the > > agents - pretty much when there is no complex emergence in the system.
	www.swarm.org /pipermail/modelling/2003-May/003417.html (328 words)

	ASU professor finds new twist to old theory
		By using a novel application of thermodynamics, Chamberlin successfully extended the range of the mean-field theory of ferromagnetism to accurately describe the behavior of ferromagnetic materials across a broader range of temperatures.
		The mean-field theory of ferromagnetism, created in 1907 by Pierre Weiss, was an important milestone in the development of modern physics.
		The long history of the mean-field theory and the implications of Chamberlin's findings are discussed in an accompanying Nature News and Views article by Tom Giebultowicz of Oregon State University.
	www.eurekalert.org /pub_releases/2000-11/ASU-Apfn-1511100.php (268 words)

	Variational approximations between mean field theory and the junction tree algorithm (Site not responding. Last check: 2007-10-09)
		Wiegerinck, W.A.J.J. Variational approximations between mean field theory and the junction tree algorithm.
		We show that the method bridges the gap between the standard mean field approximation and the exact junction tree algorithm.
		From the generalised mean field equations we derive rules to simplify the approximation in advance without affecting the potential accuracy of the model class.
	www.nici.ru.nl /Publications/2000/14452.html (188 words)

	[Swarm-Modelling] Mean Field Theory
		Incidently, as another illustration of the difference between mean field and panmictic, I introduce a model called EcoLab-- as a theoretical device in my "Statistics of Certain Models of Evolution" paper.
		EcoLab-- turns out to be a mean field approximation of a panmictic model.
		A mean field approximation is really only valid when > > > > the effect of all agents is equivalent to the sum (or average) of the > > > > agents - pretty much when there is no complex emergence in the system.
	www.swarm.org /pipermail/modelling/2003-May/003420.html (742 words)

	Statistical mechanics
		Statistical mechanics is the application of statistics, which includes mathematical tools for dealing with large populations, to the field of Mechanics, which is concerned with the motion of particles or objects when subjected to a force.
		It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in every day life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum).
		For instance, the macroscopic magnetization (extensive) is the derivative of U with respect to the (intensive) magnetic field, and the pressure (intensive) is the derivative of U with respect to volume (extensive).
	www.brainyencyclopedia.com /encyclopedia/s/st/statistical_mechanics_1.html (956 words)

	Mean-field theory and phase transitions (Site not responding. Last check: 2007-10-09)
		Mean-field theory, dating back to Curie, Weiss and Ginzburg-Landau, is one of the most common approaches to the study of phase transitions in physical systems.
		The basic underlying idea is that the complicated interactions that each element of a complex system is subjected to by its neighbors can be replaced by the interaction with an effective (or mean) field.
		It has been a common belief that the "mean-field predictions" resulting from this approximation are fairly accurate in sufficiently high dimensions but, except perhaps for the results of Hara-Slade and Aizenman-Barsky-Fernandez concerning the critical exponents in high-dimensional percolation/Ising model, very little of this belief has been mathematically justified.
	www.math.ucla.edu /~biskup/Summary/MFT.html (232 words)

	Recent Publications
		Renormalized perturbation theory is reviewed and there is a discussion of the extent to which the parameters of the standard models should be considered as quantities which have already been renormalized.
		Checks on the results using the exact diagonalization method for solving the dynamical mean field theory suggest that the linearized form is a very good approximation with errors of less than 5%.
		We derive a Ward identity and a renormalized form of the perturbation theory that encompasses both the weak and strong coupling regimes and show that the chi/gamma ratio is 8/3 (chi is the total susceptibility, spin plus isospin), independent of the interaction U and in agreement with the NRG calculations.
	www.ma.ic.ac.uk /~ahewson/recpub.html (1747 words)

	Introduction: The Mean Field Theory for Macroionic Interactions
		Such discrepancies raise concern about mean field theory's broader application to macroionic problems as diverse as protein folding, DNA complexation, and the stability of industrial suspensions.
		Since the goal of this Article is to assess constraints on theory imposed by experimental measurements of colloidal interactions, it is worthwhile to review the theory's principal approximations.
		In particular, the conventional mean field approximation replaces the functional integral in (3) with its integrand evaluated for the distribution
	www.physics.nyu.edu /~dg86/granadab/node1.html (660 words)

	[UAI] book announcement - Advanced Mean Field Methods Theory and Practic
		For more information please visit http://mitpress.mit.edu/catalog/item/default.asp?sid=5CEC3656-296C-4C48-B6E3-6BDFAC7EBADDandttype=2andtid=3847 Advanced Mean Field Methods Theory and Practice edited by Manfred Opper and David Saad A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large.
		One of the simplest approximations is based on the mean field method, which has a long history in statistical physics.
		Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.
	www.mail-archive.com /uai@cs.orst.edu/msg01427.html (321 words)

	Physics Department Talk (Site not responding. Last check: 2007-10-09)
		In this theory the nucleus is described as a system of point-like nucleons (Dirac spinors) coupled to mesons and to the photons.
		Recently, we have developed the Cranked Relativistic Hartree-Bogoliubov theory without and with approximate particle number projection by means of the Lipkin-Nogami method as an extension of Relativistic Mean Field theory with pairing correlations to the rotating frame.
		The applicability of this theory to the description of rotating nuclei has been studied in detail on the example of superdeformed bands in even-even nuclei of the A~190 mass region.
	www.physics.nd.edu /Talks/Fall2000/NUC_Nov13_2000.htm (262 words)

	Publications List of Gabriel Kotliar
		Dynamical Mean Field Theory of the Antiferromagnetic Metal to Antiferromagnetic Insulator Transition: R.
		The Mean Field Theory of the Mott Hubbard Transition:
		Mean Field Theories of Cuprate Superconductors: A Systematic Analysis, M.
	www.physics.rutgers.edu /~kotliar/Publication1.htm (2880 words)

	Ferromagnetism
		This magnetization as a function of the external field is described by a hysteresis curve.
		As the temperature increases, thermal oscillation, or entropy, competes with the ferromagnetic tendency for dipoles to align.
		There, it was first clearly shown that mean field theory approaches failed to predict the correct behavior at the critical point (which was found to fall under a universality class that includes many other systems, such as liquid-gas transitions), and had to be replaced by renormalization group theory.
	neodymiummagnets.info /ferromagnetism.php (1040 words)

	vitae22
		Theory of the Electronic Structure of Correlated Materials in Workshop on Opportunities in Materials Theory 2000 Organized by the National Science Foundation, Washinton DC, October 4-6, 2000.Foundation, Washinton DC, October 4-6, 2000.
		Dynamical Mean Field Theory of the Mott Transition 5 Lectures delivered at the Third Training Course in the Physics of Correlated Electron Systems and High-Tc Superconductors International Institute for Advanced Scientific Studies "E.R. Caianiello" Vietri sul Mare, Salerno, Italy September 20-25 (1998).
		Dynamical Mean Field Theory of the Mott transition.
	www.physics.rutgers.edu /~kotliar/vitae21 (1988 words)

	Abstract for HU-TFT-96-15 (Site not responding. Last check: 2007-10-09)
		A Dynamical Mean Field Theory for the Study of Surface Diffusion Constants
		In the present theory, the average jump rate and the susceptibility factor appearing are evaluated through Monte Carlo simulations, while the memory functions are approximated by the known results for a Langmuir gas model.
		This leads to a dynamical mean field theory (DMF) for collective diffusion, while approximate correlation effects beyond DMF are included for tracer diffusion.
	www.physics.helsinki.fi /tft/abstracts/96/42.html (158 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		The sp(3,R) mean field approximation describes collective nuclear rotation in a symplectic density matrix formalism.
		The mean field approximation restricts the densities to a coadjoint orbit of the canonical transformation group Sp(3,R).
		The cranked anisotropic oscillator and Riemann ellipsoid model are special cases of symplectic mean field theory.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20527707 (317 words)

	APS - 2005 APS March Meeting PostDeadline - Event - Decoupling methods for the solution of the dynamical mean field ... (Site not responding. Last check: 2007-10-09)
		The use of equation of motion decoupling methods as impurity solvers to be used in conjunction with the dynamical mean field self-consistency condition for the solution of lattice models is explored.
		By comparing the impurity solver to exact diagonalization results and applying it to lattice models like Hubbard model and Periodic Anderson model it is shown that the method could be a cheap alternative to computationally demanding methods like quantum Monte Carlo.
		The method works in a large range of parameters and promises to be useful in combination with density functional theory for the study of strongly correlated materials.
	meetings.aps.org /Meeting/MAR05/Event/23123 (168 words)

	Theory of continuum percolation II. Mean field theory (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Abstract: I use a previously introduced mapping between the continuum percolation model and the Potts fluid to derive a mean field theory of continuum percolation systems.
		This is done by introducing a new variational principle, the basis of which has to be taken, for now, as heuristic.
		The critical exponents obtained are fi = 1, fl = 1 and = 0:5, which are identical with the mean field exponents of lattice percolation.
	citeseer.ist.psu.edu /78479.html (272 words)

	SBF Glossary: Me., ME to MHz
		An average field used as an approximation in mean field.
		Basically, the approach is to treat the field as if it had the same value everywhere, a mean field value, so that in effect the field is reduced to a simple variable.
		The country was in the grip of economic depression when Lyon set about gathering the means with which to establish her institution.'' This is mild understatement.
	www.plexoft.com /SBF/M02.html (8472 words)

	4.3.1 Ferromagnetism
		You may view it as a closed circle, where cause and effect loose their meaning to some extent, and where a calculation produces some results that are fed back to the beginning and repeated until some parameter doesn't change anymore.
		as an internal field, we write it as a superposition of the external field H and a field stemming from the internal magnetic polarization J:
		We now identify the Weiss field with the magnetic polarization that is caused by it.
	www.tf.uni-kiel.de /matwis/amat/elmat_en/kap_4/backbone/r4_3_1.html (1253 words)

	saul96a Abstract (Site not responding. Last check: 2007-10-09)
		Saul, L.K., Jaakkola, T. and Jordan, M.I. "Mean Field Theory for Sigmoid Belief Networks", Volume 4, pages 61-76.
		Abstract: We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics.
		Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence.
	www.cs.washington.edu /research/jair/abstracts/saul96a.html (90 words)

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