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Topic: Ising model

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Ernst Ising

Phase transition

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	News Release - Ising Model
		The best-studied model in science to discuss these phase changes and, indeed, a wide variety of changes in state (neural networking, protein folding, flocking birds, beating heart cells, questions of economics, and more) is the Ising Model, developed by Ernst Ising in 1926 as part of his Ph.D. dissertation.
		Yet the continued application of Ising's model -- more than 8,000 papers published between 1969 to 1997 -- has tempted many scientists to extend the grid's usefulness by developing a proof in three dimensions, the realm in which most real-world problems take place.
		The modeler was restricted to menial jobs and, though he survived World War II and taught afterwards in the United States, never published again.
	www.sandia.gov /media/NewsRel/NR2000/ising.htm (662 words)

	Chapter 1: Spin Models
		Part of the model may consist in the assertion that certain aspects of the model may be described mathematically and exhibit certain mathematical relations, thereby allowing properties of the model to be deduced on the basis of results established by mathematicians.
		Ising studied the simplest possible model consisting simply of a linear chain of spins, and showed that for this 1-dimensional case there is no (non-zero) critical temperature (i.e., the spins become aligned only at T = 0).
		In 1944 the physicist Lars Onsager, studying the 2-dimensional Ising model on a square lattice, was able to demonstrate by analytical means the existence of a phase transition in the model, a result considered to be a landmark in the physics of critical phenomena.
	www.hermetic.ch /compsci/thesis/chap1.htm (6408 words)

	The Ising model
		Using this version of the Ising model, we show that the nature of transcategorial change between a lexical state and a functional state can be described by a first-order phase transition.
		Within the Ising model, the energy is specific to the temperature of the system and can be controlled explicitly by tuning the system relative to a critical point where the two biases balance.
		In a standard Ising model the number of potential degenerate states is equal for all constituents.
	www.cecm.sfu.ca /~thalie/PhD/node16.html (1259 words)

	4.4.2 Ising Model
		The Ising model is the simplest model for ferromagnetism that predicts phase transitions and critical phenomena.
		This model, introduced by Lenz in 1920 [Lenz:20a], was solved in one dimension by Ising in 1925 [Ising:25a], and in two dimensions by Onsager in 1944 [Onsager:44a].
		For the Ising model, the blocked spin value is given the value taken by the majority of the 4 plaquette spins, with a random tie-breaker for the case where there are 2 spins in either state.
	zikova.cvut.cz /parallel/pcw/node44.html (1366 words)

	Exploring the Three-Dimensional Ising Model (Site not responding. Last check: 2007-11-05)
		In the Ising model, these spins are arranged in a three-dimensional lattice, with one spin per lattice point.
		The theory behind the Ising model assumes that the lattice size is infinite.
		Another property of the model is that groups of aligned spins form magnetic domains, called clusters, similar to those found in magnetic solids, such as iron.
	www.hope.edu /academic/physics/reu00/AC_use.html (1250 words)

	Ernest Ising Obituary
		The most striking success of the model is accompanied by the search for the phase transition between the ferromagnetic and the paramagnetic state.
		Today, the Ising model is a widely used standard model of statistical physics.
		The Ising Conference room is located in Bradley University's Olin Hall of Science where visitors can view framed copies of Ising's dissertation in both German and English along with photographs of Ernst and Jane through the years.
	www.bradley.edu /las/phy/personnel/isingobit.html (867 words)

	Introduction to the Ising Model (Site not responding. Last check: 2007-11-05)
		The Ising Model is one of the pillars of statistical mechanics.
		As a system of +/- spins, it is a model for magnetism: like iron, there is a temperature (the Neel point) above which the magnetization "melts" away.
		Thought of as sites either occupied or vacant (1/0) on a lattice, it is a model for the liquid-gas transition: dense regions of occupied "liquid" are surrounded by dilute regions of mostly "gas".
	www.physics.cornell.edu /sethna/teaching/sss/ising/intro.htm (257 words)

	Ising Model
		This is done by random correlation of numbers, and a 3 sweep process of ising model calculations being performed on the lattice.
		The first step in the modeling process is assigning a 9801 array with random spins to designate a 99x99 two dimensional array lattice.
		Ising model calculations are now performed on the lattice to achieve equalization among the spins.
	www.aspire.cs.uah.edu /aspire/isingmodel.html (1489 words)

	Dr. Ernest Ising (Site not responding. Last check: 2007-11-05)
		Ernest Ising was Professor of Physics at Bradley from 1948-1976 and Professor Emeritus until his death.
		Ising is recognized in the worldwide scientific community for his development of the Ising Model.
		This model came to be known as the famous Ising Model.
	www.bradley.edu /las/phy/personnel/ising.html (396 words)

	Ising applet (Site not responding. Last check: 2007-11-05)
		One way in which physicists can gain insight into these difficult systems is by constructing idealised models which, it is hoped, will exhibit some of the interesting features of real systems but are simpler to study.
		Perhaps the most famous of these simplified models is the two-dimensional Ising model which may be used to model the behavior of simple magnets.
		The model consists of a set of magnetic spins arranged on a regular square lattice.
	www.phy.syr.edu /courses/ijmp_c/Ising.html (436 words)

	Klaus Kannemann Thesis Summary Ising Model
		The thesis is a study on the linear Ising model and the related linear lattice fluid.
		The ferromagnetic behavior of the straight-line version of the linear model with simplified long-range interaction potential is demonstrated with mathematical rigor, whereby we use results from the theory of measure and integration.
		Yet the venerable Ising Model continues the be one of the leading paradigms of cooperative phenomena, and it is precisely for its inherent similarity with neural nets that the model has been adapted for the study and simulation of emergent phenomena and behavior in the realm of Artificial Life -- those of the Connectionist School,
	www3.sympatico.ca /kkanne/thesis.htm (689 words)

	Ernst Ising and the Ising model
		Ising was dismissed from his job as a civil servant
		Hansmann, Ulrich H.E. Ising models and helix-coil transition in biomolecules
		Ising interaction of four separate spins in self-assembled supramolecular [2
	www.physik.tu-dresden.de /itp/members/kobe/isingconf.html (248 words)

	The Ising Model (Site not responding. Last check: 2007-11-05)
		This model has a two-dimensional solution,(the one we will use), and was discovered by Onsager in 1944.
		This is the first step in correlating both the Ising model and a simple language model.
		If the underlying research is correct, then the eventual outcome of this process is that many vocables pass from a stage in which we typically can explain them by definition or ostension, to a stage in which virtually all of us can use them but none of us can understand them.
	www.cecm.sfu.ca /~thalie/PhD/node67.html (220 words)

	Phase transitions in magnetics (Site not responding. Last check: 2007-11-05)
		In the XY model spins rotate in a plane.
		In the Ising model spins have only two possible states +-1 (up or down).
		Onsager solved exectly the 2D Ising problem in 1944, showing that it had a phase transition.
	www.people.nnov.ru /fractal/perc/Ising.htm (445 words)

	Ising Model WWW References (Site not responding. Last check: 2007-11-05)
		This is a first attempt at sorting through some of the Ising Model material available on the World Wide Web.
		The model of flipping individual spin sites would appear to be an attractive "sample problem" for Java practitioners.
		The Potts Model is a genneralization of the Ising Model in which the spins take a large set of values, such as {-3,-2,-1,1,2,3} in place of the simple {+1,-1} in the Ising Model.
	oscar.cacr.caltech.edu /Hrothgar/Ising/references.html (303 words)

	HCPCP -- Ising Model Project (Site not responding. Last check: 2007-11-05)
		Section I--Introduction to models for ferromagnetism, beginning with a fairly realistic model based on the Heisenberg exchange interaction and reducing the complexity of the problem (while retaining the possibility of a ferromagnetic ground state) until one arrives at the Ising model.
		Section II--The structure of the 2-d Ising model is probed to establish that a brute force summation of the partition function is out of the question.
		Section VI applies the Monte Carlo method to the statistical sums associated with the 2-d Ising model and is appropriate as the 4th week assignment.
	www.haverford.edu /physics-astro/Roelofs/HCPCP/Ising/Desc.html (863 words)

	SIM: Ising Model
		In this model we change from one state to another by flipping the spin at a single site and the associated change of energy is given by
		In the 2-D square lattice model, there are only 4 nearest neighbours, and therefore there are only 5 possible values for the spin-flip probability.
		An implementation of this Ising Model is done in the root macro ising2d.C.
	hepwww.ph.qmw.ac.uk /~traynor/sim/week6/ising.html (682 words)

	Ising Model
		It allows all the interesting properties of the lattice model to be altered.
		The Correlation Length is an approximate measure of the size of uniformly-pointing patches within the field; in a model such as this, the correlation length grows infinitely large (or at least grows to the maximum floating point number available to the system) when the system's temperature drops below the critical temperature.
		The source code for the Ising model applet may be downloaded.
	www.rpi.edu /~limc/applets/ising (1735 words)

	Exact solutions of the Ising model in 1 and 2 dimensions
		Exact solutions of the Ising model are possible in 1 and 2 dimensions and can be used to calculate the exact critical exponents for the two corresponding universality classes.
		While the one-dimensional Ising model is a relatively simple problem to solve, the two-dimensional Ising model is highly nontrivial.
		It was only the pure mathematical genius of Lars Onsager that was able to find an analytical solution to the two-dimensional Ising model.
	www.nyu.edu /classes/tuckerman/stat.mech/lectures/lecture_26/node2.html (423 words)

	Ising Model Files (Site not responding. Last check: 2007-11-05)
		This Mathematica program is used to calculate the partition function coefficients of the 2-dimensional Ising model.
		Notice these are NOT symmetric from end to end because a antiferromagnetic (checkerboard) pattern will not fit onto the odd lattice beacuse of the periodic boundary conditions.
		Note the first term in each file is 0.6931471805599453 = ln(2) since the ground state of the ferromagnetic Ising model is 2-fold degenerate (all spins up or all spins down).
	www.colorado.edu /physics/phys7230/phys7230_sp03/ising (316 words)

	Ising-Model (Site not responding. Last check: 2007-11-05)
		Every little box of the spin field represents one of the two possible states S
		You can control the temperature either by typing a (positive) real number into the temperature field or by adjusting the thermometer by mouse.
		The critical temperature of the two dimensional Ising model is T
	bartok.ucsc.edu /peter/java/ising/keep/ising.html (407 words)

	Random bond Ising model
		In the random system, there are preferred positions for the domain wall, in which the bonds that are broken by the wall are chosen to lie on ``weak'' links.
		This is the simplest example of a topological defect, which is defined as a configuration of an order parameter in which the states at infinity are non-trivially ``twisted''.
		In fact, such topological defects often lead to elastic models of the kind we will discuss here.
	online.itp.ucsb.edu /online/lnotes/balents/node9.html (469 words)

	Ising Model - Closed chain (Site not responding. Last check: 2007-11-05)
		For simplicity consider the closed chain Ising model - a string of n neighbor coupled spin sites
		The energy of the system is given by the sum of the internal interaction energies of neighboring spin states and the energy of interaction of the set of states with an external field, which for the Ising model is taken to be a sum of spin-field energies.
		Thus, with the spin-spin coupling given by -Q and the spin-field constant -R, the energy in the Ising model is given by
	www.realtime.net /~drwolf/papers/dissertation/node55.html (100 words)

	Ising Java Applet (Site not responding. Last check: 2007-11-05)
		Spin up and spin down in a 2-D 60x60 ferromagnetic Ising system are represented below by
		The applet gives Monte-Carlo updates of the lattice at a rate of about 3 per second (you can alter the applet code to get faster updates).
		Play with it until you can not stand it any longer.
	www2.truman.edu /~velasco/ising.html (124 words)

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