Michael Creutz. Deterministic ising dynamics. Annals of Physics, 167:62--72, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....have one predecessor. Usually the recurrence time is astronomical because there are so many variables and few conservation laws, but for the specific system shown in figure 2 10, the period is a mere 40926 steps. Cellular automata are well suited for doing dynamical simulations of Ising models [19, 20, 93], where each cell contains one spin (1 = up, Gamma1 = down) Many variations are possible, and figure 2 11 shows one such model that is a reversible, second order CA which conserves the usual Ising Hamiltonian, H = GammaJ i;j s i s j ; 2.1) where J is a coupling constant, and Delta ....

.... proper (consisting of featureless particles) and the latter will be the heat bath (consisting of energy tokens) The tokens are sometimes called demons following Creutz, who originated the general idea of introducing additional degrees of freedom to enable microcanonical Monte Carlo simulation [19, 20]. The particles and the energy tokens move from cell to cell under an appropriate CA rule as described below. The lattice gases can be viewed as residing in parallel spaces (0 and 1) and the system logically consists of three regions (AB, C, and D) as shown in figure 3 1(a) The circle ....

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Michael Creutz. Deterministic ising dynamics. Annals of Physics, 167:62--72, 1986.

....paradigm. Inspired by Fredkin s billiard ball model of computation[19] Margolus arrived in 1983 at a very simple computation universal ica[41] that is suggestive of how a computer could in principle be built out of microscopic mechanics. At about the same time, Vichniac[83] and Creutz[13] pioneered the used of cellular automata for the microcanonical modeling of Ising spin systems. The introduction of dedicated cellular automata machines[71] encouraged much new experimental work on ica, and stimulated further theoretical developments. For instance, according to Pomeau, seeing ....

....tangible aspect (cf. 73] to materialize itself. For the above reasons, and because they lend themselves to very efficient computer simulations, ica are an ideal medium for the qualitative study of the connections between microscopic mechanics and statistical mechanics on one hand (cf. [43,77,85,13]) and between statistical mechanics and macroscopic mechanics on the other (cf. 88] They are also suitable for the the modeling of an increasingly important type of generalized mechanical activity, namely computation[43] In physics, additive invariants, whether represented by mechanical ....

Creutz, Michael, "Deterministic Ising Dynamics," Annals of Physics 167 (1986), 62--76.

....data, by in situ illumination. Fig. 3 shows a stage in the cooling of a 3 D Ising spin system (a model of ferromagnetic materials) solid matter represents the spin up phase, while the spin down phase is represented by the remaining empty space. The data come from a microcanonical simulation[2] carried out at a few frames per second by a cam 8 machine (see x3) Here we are not concerned with the nature of the system being Figure 3: A stage in the cooling of an Ising spin system. Solid matter represents the spin up phase. 3 D rendering by verbatim simulated illumination. modeled, but ....

Creutz, Michael, "Deterministic Ising Dynamics," Annals of Physics 167 (1986), 62--76.

....paradigm. Inspired by Fredkin s billiard ball model of computation[19] Margolus arrived in 1983 at a very simple computation universal ica[41] that is suggestive of how a computer could in principle be built out of microscopic mechanics. At about the same time, Vichniac[83] and Creutz[13] pioneered the used of cellular automata for the microcanonical modeling of Ising spin systems. The introduction of dedicated cellular automata machines[71] encouraged much new experimental work on ica, and stimulated further theoretical developments. For instance, according to Pomeau, seeing (at ....

....each configuration belongs to a definite symmetry class (a normal subgroup of the group itself) all the points of an orbit belong to the same symmetry class, which is thus a conserved quantity. 19 This is the uniform measure, which gives equal weight to all configurations. one hand (cf. [43, 77, 85, 13]) and between statistical mechanics and macroscopic mechanics on the other (cf. 88] They are also suitable for the the modeling of an increasingly important type of generalized mechanical activity, namely computation[43] In physics, additive invariants, whether represented by mechanical ....

Creutz, Michael, "Deterministic Ising dynamics," Annals of Physics 167 (1986), 62--76.

....that of spins down. Also the interaction energy between two adjacent spins has only two possible values, depending on whether or not the spins point in the same direction. The essential statistical mechanical aspects of the material are captured by the following cellular automaton dynamics (cf. [2]) At each time step, 1 a spin will flip (change state) only if two of its neighbors are pointing up and the other two are pointing down (Fig. 4b) It is easy to verify that, besides being local and uniform, this dynamics is microscopically reversible and satisfies energy conservation. In ....

Creutz, Michael, "Deterministic Ising Dynamics," Annals of Physics 167 (1986), 62--76.

....(non periodic, non chaotic) regimes, such as long 11 There are some results concerning computation in CA and phase transitions. Individual CA have been known for some time to exhibit phase transitions with the requisite divergence of correlation length required for infinite memory capacity. [2] 12 In the context of continuous state dynamical systems, it has been shown that there is a direct relationship between intrinsic computational capability of a process and the degree of randomness of that process at the phase transition from order to chaos. Computational capability was ....

M. Creutz. Deterministic Ising dynamics. Ann. Phys., 167:62, 1986.

....processing in terms of (1) particles that transmit information over 4 There are several direct inferences concerning computation in CAs and phase transitions that can be drawn from existing results. For example, individual CAs have been known for some time to exhibit phase transitions [5] with the requisite divergence of correlation length required for infinite memory capacity. long space time distances and (2) particle particle interactions that perform logical operations [6] A summary of this type of analysis of the GKL rule in terms of particles is given in [23] Let us ....

M. Creutz. Deterministic Ising dynamics. Ann. Phys., 167:62, 1986.

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M. Creutz. Deterministic Ising dynamics. Ann. Phys., 167:62, 1986.

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