ZIB

1

Digitale Medien

Exact results for the two-dimensional, two-component plasma atΓ=2 in doubly periodic boundary conditions (1990)

Forrester, P. J.

Springer

Journal of statistical physics 61 (1990), S. 1141-1160

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Two-component plasma ; determinants ; Yang-Lee theory

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract The two-dimensional, two-component plasma is considered in doubly periodic boundary conditions with the positive and negative charges confined to separate interlacing rectangular lattices. It is shown that at the special couplingΓ=2, on a lattice of 2M 1×2M 2 sites, the grand partition function can be written as a double integral over a product of determinants of dimension 2M 2×2M 2. On the basis of a conjecture regarding the zero distribution of the grand partition function, the large-M 2 behavior of the determinant is given and the pressure evaluated exactly.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01014369

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext

2

Digitale Medien

A testbench for the nested dipole hypothesis of Kosterlitz and Thouless (1995)

Alastuey, A. ; Forrester, P. J.

Springer

Journal of statistical physics 79 (1995), S. 503-523

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Kosterlitz-Thouless transition ; Coulomb gas ; renormalization equations ; correlations ; exact solution

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract We consider the two-dimensional one-component plasma without a background and confined to a half-plane near a metal wall. The particles are also subjected to an external potential acting perpendicular to the wall with an inverse-power-law Boltzmann factor. The model has a known solvable isotherm which exhibits a Kosterlitz-Thouless-type transition from a conductive to an insulator phase as the power law is varied. This allows predictions of theoretical methods of analyzing the Kosterlitz-Thouless transition to be compared with the exact solution. In particular, we calculate the asymptotic density profile by resumming its low-fugacity expansion near the zero-density critical coupling in the insulator phase, and solving a mean-field equation deduced from the first BGY equation. Agreement with the exact solution is obtained. As the former calculation makes essential use of the nested dipole hypothesis of Kosterlitz and Thouless, the validity of this hypothesis is explicitly verified.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02184869

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext

3

Digitale Medien

The two-dimensional Coulomb gas on a sphere: Exact results (1992)

Forrester, P. J. ; Jancovici, B. ; Madore, J.

Springer

Journal of statistical physics 69 (1992), S. 179-192

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Coulomb gas ; solvable models ; Dirac equation ; curved space

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract At the special value of the reduced inverse temperatureΓ=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01053789

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext

4

Digitale Medien

The two-dimensional two-component plasma plus background on a sphere: Exact results (1996)

Forrester, P. J. ; Jancovici, B.

Springer

Journal of statistical physics 84 (1996), S. 337-357

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Coulomb gas ; solvable models ; finite-size corrections

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract An exact solution is given for a two-dimensional model of a Coulomb gas, more general than the previously solved ones. The system is made up of a uniformly charged background, positive particles, and negative particles, on the surface of a sphere. At the special value Γ=2 of the reduced inverse temperature, the classical equilibrium statistical mechanics is worked out: the correlations and the grand potential are calculated. The thermodynamic limit is taken, and as it is approached the grand potential exhibits a finite-size correction of the expected universal form.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02179646

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext

5

Digitale Medien

Exact Finite-Size Study of the 2D OCP at Γ=4 and Γ=6 (1999)

Téllez, G. ; Forrester, P. J.

Springer

Journal of statistical physics 97 (1999), S. 489-521

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Coulomb gas ; one-component plasma ; symmetric polynomials ; finite-size corrections ; second-moment sum rules

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract An exact numerical study is undertaken into the finite-N calculation of the free energy and distribution functions for the two-dimensional one-component plasma. Both disk and sphere geometries are considered, with the coupling Γ set equal to 4 and 6. Extrapolation of our data for the free energy is consistent with the existence of a universal term (χ/12)logN, where χ denotes the Euler characteristic of the surface, as predicted theoretically. The exact finite-N density profile is shown to give poor agreement with the contact theorem relating the density at contact and potential drop to the pressure in the thermodynamic limit. This is understood theoretically via a known finite-N version of the contact theorem. Furthermore, the ideas behind the derivation of the latter result are extended to give a sum rule for the second moment of the pair correlation in the finite disk, which in the thermodynamic limit converges to the Stillinger–Lovett result.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1023/A:1004654923170

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext

6

Digitale Medien

Vicious random walkers in the limit of a large number of walkers (1989)

Forrester, P. J.

Springer

Journal of statistical physics 56 (1989), S. 767-782

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Random walk ; Coulomb gas ; orthogonal polynomials

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract The vicious random walker problem on a line is studied in the limit of a large number of walkers. The multidimensional integral representing the probability that thep walkers will survive a timet (denotedP t (p) ) is shown to be analogous to the partition function of a particular one-component Coulomb gas. By assuming the existence of the thermodynamic limit for the Coulomb gas, one can deduce asymptotic formulas forP t (p) in the large-p, large-t limit. A straightforward analysis gives rigorous asymptotic formulas for the probability that after a timet the walkers are in their initial configuration (this event is termed a reunion). Consequently, asymptotic formulas for the conditional probability of a reunion, given that all walkers survive, are derived. Also, an asymptotic formula for the conditional probability density that any walker will arrive at a particular point in timet, given that allp walkers survive, is calculated in the limitt≫p.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01016779

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext

7

Digitale Medien

Yang-Lee theory and the conductor-insulator transition in asymmetric log-potential lattice gases (1990)

Forrester, P. J.

Springer

Journal of statistical physics 60 (1990), S. 203-220

zur Merkliste hinzufügen auf der Merkliste

Details

ISSN: 1572-9613

Schlagwort(e): Conductor-insulator transition ; Yang-Lee theory ; exact solvability

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract A feature of a conducting phase at low density is that there is a singularity in the fugacity expansion of the pressure, whereas the same expansion in the insulating phase gives an analytic series. The Yang-Lee characterization of a phase transition thus implies that in the conducting phase the zeros of the grand partition function must pinch the real axis in the complex scaled fugacity (ξ) plane at ξ=0, whereas in the insulating phase a neighborhood of ξ=0 must be zero free. Exact and numerical calculations are presented which suggest that for two-component log-potential lattice gases in one dimension with dimensionless couplingΓ, the zeros pinch the point ξ=0 forΓ〈2, while forΓ⩾2 a neighborhood of ξ=0 is zero free. The conductor-insulator transition therefore takes place atΓ=2 independent of the density and other parameters in the model.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF01013674

Permalink

Bibliothek	Standort	Signatur	Band/Heft/Jahr	Verfügbarkeit

Andere fanden auch interessant ...

Artikel (Nationallizenzen)

Volltext