scholarly journals The naming game in language dynamics revisited

2014 ◽  
Vol 51 (A) ◽  
pp. 139-158
Author(s):  
Nicolas Lanchier
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Point Of View ◽  
Mean Field Approximation ◽  
Complete Graphs ◽  
Naming Game ◽  
Limiting Behavior ◽  
Linguistic Convention ◽  
Regular Lattices ◽  
The One

In this article we study a biased version of the naming game in which players are located on a connected graph and interact through successive conversations in order to select a common name for a given object. Initially, all the players use the same word B except for one bilingual individual who also uses word A. Both words are attributed a fitness, which measures how often players speak depending on the words they use and how often each word is spoken by bilingual individuals. The limiting behavior depends on a single parameter, ϕ, denoting the ratio of the fitness of word A to the fitness of word B. The main objective is to determine whether word A can invade the system and become the new linguistic convention. From the point of view of the mean-field approximation, invasion of word A is successful if and only if ϕ > 3, a result that we also prove for the process on complete graphs relying on the optimal stopping theorem for supermartingales and random walk estimates. In contrast, for the process on the one-dimensional lattice, word A can invade the system whenever ϕ > 1.053, indicating that the probability of invasion and the critical value for ϕ strongly depend on the degree of the graph. The system on regular lattices in higher dimensions is also studied by comparing the process with percolation models.

scholarly journals The naming game in language dynamics revisited

2014 ◽  
Vol 51 (A) ◽  
pp. 139-158
Author(s):  
Nicolas Lanchier
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Point Of View ◽  
Mean Field Approximation ◽  
Complete Graphs ◽  
Naming Game ◽  
Limiting Behavior ◽  
Linguistic Convention ◽  
Regular Lattices ◽  
The One

In this article we study a biased version of the naming game in which players are located on a connected graph and interact through successive conversations in order to select a common name for a given object. Initially, all the players use the same word B except for one bilingual individual who also uses word A. Both words are attributed a fitness, which measures how often players speak depending on the words they use and how often each word is spoken by bilingual individuals. The limiting behavior depends on a single parameter, ϕ, denoting the ratio of the fitness of word A to the fitness of word B. The main objective is to determine whether word A can invade the system and become the new linguistic convention. From the point of view of the mean-field approximation, invasion of word A is successful if and only if ϕ > 3, a result that we also prove for the process on complete graphs relying on the optimal stopping theorem for supermartingales and random walk estimates. In contrast, for the process on the one-dimensional lattice, word A can invade the system whenever ϕ > 1.053, indicating that the probability of invasion and the critical value for ϕ strongly depend on the degree of the graph. The system on regular lattices in higher dimensions is also studied by comparing the process with percolation models.

scholarly journals Testing the Monte Carlo–mean field approximation in the one-band Hubbard model

2014 ◽  
Vol 90 (20) ◽  
Author(s):  
Anamitra Mukherjee ◽  
Niravkumar D. Patel ◽  
Shuai Dong ◽  
Steve Johnston ◽  
Adriana Moreo ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Hubbard Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
The One

The Glauber and Metropolis Transition Rates on the Stationary States of the Ising Model

1997 ◽  
Vol 11 (13) ◽  
pp. 565-570
Author(s):  
G. L. S. Paula ◽  
W. Figueiredo
Keyword(s):  
Ising Model ◽  
Nearest Neighbor ◽  
Mean Field ◽  
Field Approximation ◽  
Two Dimensions ◽  
Mean Field Approximation ◽  
Stationary States ◽  
Transition Rates ◽  
The Mean ◽  
The One

We have applied the Glauber and Metropolis prescriptions to investigate the stationary states of the Ising model in one and two dimensions. We have employed the formalism of the master equation to follow the evolution of the system towards the stationary states. Although the Glauber and Metropolis transition rates lead the system to the same equilibrium states for the Ising model in the Monte Carlo simulations, we show that they can predict different results if we disregard the correlations between spins. The critical temperature of the one-dimensional Ising model cannot even be found by using the Metropolis algorithm and the mean field approximation. However, taking into account only correlations between nearest neighbor spins, the resulting stationary states become identical for both Glauber and Metropolis transition rates.

A NONLINEAR MODEL OF THE COLLECTIVE SPONTANEOUS EMISSION BY A SPIN SYSTEM

1996 ◽  
Vol 10 (27) ◽  
pp. 1339-1347
Author(s):  
SALOMON S. MIZRAHI ◽  
VICTOR V. DODONOV ◽  
DINO OTERO
Keyword(s):  
Spontaneous Emission ◽  
Spin System ◽  
Mean Field ◽  
Field Approximation ◽  
Secondary Emission ◽  
Mean Field Approximation ◽  
Quantum Master Equation ◽  
Pure Spin ◽  
New Equation ◽  
The One

We propose a nonlinear quantum master equation, which results in the nonlinear Bloch-like equations, similar to those which are used usually to describe the collective spontaneous emission by a system of two-level atoms or a spin system in a magnetic field. On the one hand, the new equation is the unique simplest homogeneous and nonsingular generalization of the linear master equations for quantum systems in the finite-dimensional Hilbert space. On the other hand, it corresponds to the mean-field approximation, and in this form it can be used for a larger class of systems. Our equations describe both triggered and pure spin emission processes (when the population is completely inverted), and their solutions show the occurrence of secondary emission peaks, as observed in experiments.

A TWO-BAND SUPERCONDUCTOR WITH A NARROW BAND NEAR THE FERMI LEVEL

1988 ◽  
Vol 02 (05) ◽  
pp. 679-680
Author(s):  
V. P. Galaiko
Keyword(s):  
Fermi Level ◽  
Narrow Band ◽  
Mean Field ◽  
Wide Band ◽  
Field Approximation ◽  
System Stability ◽  
Mean Field Approximation ◽  
Strong Electron ◽  
The Mean ◽  
The One

The modern theory of conventional superconductivity is based upon the concept of quantum states with broken gauge symmetry providing non-zero values for the so-called "anomalous averages" [Formula: see text], [Formula: see text]. Being applied to the simplest Gorikov-like semiphenomenological electronic scenario for a metal superconductor, this idea (in the mean field approximation) leads towards a complete description of all properties of ordinary superconductors as a manifestation of macroscopic quantum phase coherence. Currently there exists already strong experimental evidence that the newly discovered high Tc superconductors exhibit the same quantum coherence effects including the highly characteristic quantity for these phenomena, namely the doubled electronic charge. On these grounds one can expect that the high Tc superconductors should also be described by "anomalous averages" of the same kind. The only question is whether Gorikov's scenario is still sufficient or we need a new scenario instead in order to grasp the whole situation. In the case of Gorikov's scenario one needs to explain how the strong electron-electron coupling (no matter of what origin) can be consistent with the system stability condition. Yet there is another argument in favour of a new scenario. The large variety of the new SC properties cannot be explained by a model with too limited number of physical parameters. In our dealing with the problem of a possible new scenario we have suggested that in order to understand the high T c superconductors one should not perhaps go so far as to doubt the one-particle approximation and to introduce the Hubbard-like models, RVB and so on. Taking into account the crystalline structure of perfect high T c superconductors we have assumed within the one-particle description the two overlapping bands approach which was proposed by Suhl, Mattias and Walker (USA) and Moskalenko (USSR) as early as in 1959. To obtain qualitatively new results we have suggested a sharp asymmetry between the two bands (one being practically a local energy level close to the Fermi level) and also a special structure of direct electron-electron interaction with dominating interband scattering of singlet electron pairs described by an amplitude g. As the final analysis has shown, an inevitable but comparatively small splitting of the two bands does not invalidate the results of the model. As to the peculiar structure of interaction we believe it might be explained through a strong electron-optical phonon coupling due to the Jahn-Teller-like instability manifested in tetragonal-orthorhombic transitions of HT c samples. The model just outlined can indeed yield high T c . In the mean field approximation (with two superconductivity order parameters) the order of magnitude of T c is given by T c ~ (|g|N(o)/2)2 EF where N(o) is the density of states in the wide band at the Fermi level and EF is a wide band width. There is an exponentially sharp decline of T c while overdoping or underdoping the system and there is also a broad plateau when the narrow band is filled partially (the heavy fermion situation). The other results of calculations including thermodynamics and also kinetic properties for the normal state do not contradict experiments except for the linear temperature dependence of the specific heat observed sometimes. But one must take into account that in reality all high T c superconductors are in fact disordered solutions, and it is necessary to consider the dirty alloy limit with Anderson's theorem being violated because of the narrow band existence. At the same time, as analysis shows, the mean field approximation is not good enough for the model (the small parameter is only ( log 2/|g|N(o))-1) and therefore one has to apply Green's functions technique in order to correct the results. There is also a possibility that the magnetic properties connected with localized spins (if there are any) must be taken into account as well.

scholarly journals GAMOW–TELLER SUM RULE IN RELATIVISTIC NUCLEAR MODELS

2006 ◽  
Vol 21 (12) ◽  
pp. 935-946 ◽  
Author(s):  
HARUKI KURASAWA ◽  
TOSHIO SUZUKI
Keyword(s):  
Degrees Of Freedom ◽  
Random Phase ◽  
Mean Field ◽  
Field Approximation ◽  
Point Of View ◽  
Mean Field Approximation ◽  
Sum Rule ◽  
Relativistic Mean Field ◽  
Relativistic Corrections ◽  
Gamow Teller

Relativistic corrections are investigated to the Gamow–Teller (GT) sum rule with respect to the difference between the β- and β+ transition strengths in nuclei. Since the sum rule requires the complete set of the nuclear states, the relativistic corrections come from the anti-nucleon degrees of freedom. In the relativistic mean field approximation, the total GT strengths carried by the nucleon sector is quenched by about 12% in nuclear matter, while by about 8% in finite nuclei, compared to the sum rule value. The coupling between the particle-hole states with the nucleon–antinucleon states is also discussed with the relativistic random phase approximation, where the divergence of the response function is renormalized with use of the counterterms in the Lagrangian. It is shown that the approximation to neglect the divergence, like the no-sea approximation extensively used so far, is unphysical, from the sum-rule point of view.

SPINOR BEC IN THE LARGE-N LIMIT

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4248-4255 ◽  
Author(s):  
ZHIBING LI ◽  
CHENGGUANG BAO
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Spin Coupling ◽  
Mean Field Approximation ◽  
Condensed State ◽  
Bose Einstein Condensate ◽  
Alkali Atoms ◽  
The One ◽  
Bose Einstein

The superfine structure of Bose-Einstein condensate of alkali atoms due to the spin coupling have been investigated in the mean field approximation. In the limit of large number of atoms, we obtained the analytical solution for the fully condensed states and the states with one-atom excited. It was found that the energy of the one-atom excited state could be smaller than the energy of the fully condensed state, even two states have similar total spin.

Application of the Mean-Field Approximation to the Magnetic and Superconducting Phases of Quasi-One-Dimensional Metal

2009 ◽  
Vol 152-153 ◽  
pp. 591-594 ◽  
Author(s):  
A.V. Rozhkov
Keyword(s):  
Density Wave ◽  
Spin Density Wave ◽  
Mean Field ◽  
Field Approximation ◽  
High Energy ◽  
Mean Field Approximation ◽  
One Dimensional ◽  
Ordered Phases ◽  
The Mean ◽  
The One

We research under what condition the mean-field approximation can be applied to study ordered phases of quasi-one-dimensional metal. It is shown that the mean-field treatment is indeed permissible provided that it is applied not to the microscopic Hamiltonian (subject to severe one-dimensional high-energy fluctuations), but rather to effective Hamiltonian derived at the dimensional crossover scale. The resultant mean-field phase diagram has three ordered phases: spin density wave, charge density wave, and superconductivity. The density wave orders win if the Fermi surface nests well. Outcome of competition between the intra-chain and inter-chain electron repulsion determines the type (spin vs. charge) of the density wave. The ground state becomes superconducting (with unconventional order parameter) when the nesting is poor. The superconducting mechanism relies crucially on the one-dimensional fluctuations.

scholarly journals PARITY VIOLATION AND THE MEAN FIELD APPROXIMATION FOR THE ANYON GAS

1993 ◽  
Vol 08 (20) ◽  
pp. 1909-1915 ◽  
Author(s):  
DIDIER CAENEPEEL ◽  
RICHARD MACKENZIE
Keyword(s):  
Magnetic Field ◽  
Parity Violation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Radius Of Curvature ◽  
Interparticle Separation ◽  
The Mean ◽  
The One ◽  
Self Consistency

We examine an approach to justifying the mean field approximation for the anyon gas, using the scattering of anyons. Parity violation permits a nonzero average scattering angle, from which one can extract a mean radius of curvature for anyons. If this is larger than the interparticle separation, one expects that the graininess of the statistical magnetic field is unimportant, and that the mean field approximation is good. We argue that a non-conventional interaction between anyons is crucial, in which case the criterion for validity of the approximation is identical to the one deduced using a self-consistency argument.

scholarly journals QCD ON A TREE

1995 ◽  
Vol 10 (37) ◽  
pp. 2863-2875 ◽  
Author(s):  
D.V. BOULATOV
Keyword(s):  
Phase Transition ◽  
Gauge Group ◽  
Weak Coupling ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Chiral Field ◽  
Coupling Phase ◽  
Large N ◽  
The One

We propose a model which can be regarded as a mean field approximation for pure lattice QCD and chiral field. It always possesses a phase transition between a strong-coupling phase (where it reduces to a one-plaquette integral) and a nontrivial weak-coupling one. For the U(N) gauge group, it is equivalent to some hermitian multi-matrix model. This analogy allows us to determine possible large-N critical regimes thus generalizing the Gross-Witten phase transition in the one-plaquette model.

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